Digital Filter Design-DSP

7222019 Digital Filter Design-DSP

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ibitfk îbhfk _r`nassihb F

Nùrsa h

Mibitfk Eiktar Masibhamp

afkizfti`h witd Gukt irfta M^_Ly

_rfbhfh Ndfcrfv`rtyMirant`r NFA]

G]and (II] Cdfrfbpur) Gaglar-IAAA(Q^F) FNG(Q^F)

Gaglar IAAA -

N`gguhinfti`h `n

Ginr`wfva ]da`ry fhm ]andhiquas ^`n

Fhtahhf amp Rfva _r`pfbfti`h ^`n

Nkiqua e`r Fppkiam asafrnd ih Akantr`hin ]andh`k`by

Fmvfitf N`rp`rfti`h



NH]AH]^

6 Eiktars fra Imafkky Kihafr ]iga Ihvfrifht systagslt Rdft fra Eiktars0

gt ]da ]rfhsear Euhnti`h

= Katrsquos labih w itd Lut tarw`rtd k`w pfss ndfrfntaristins

1 Rdara is Mibitfk Eiktar (Lik ihafr ]rfhse`rg)0

5 Rfrpihb

2 Rdara fra wa04 Mibitfk eiktar Masibh Ek`w Mifbrfg

9 Eihita Igpuksa asp`hsa (EI) Eiktar Masibh

6Eùriar ]rfhse`rg Gatd`m

66Rihm`w Gatd`m

6ltEraquahny ^fgpkihb Gatd`m



Eiktars fra Imafkky Kihafr ]iga Ihvfrifht systags

at



Rdft fra Eiktars0

Ih tda prasaht n`htaxt e ik tars fra systags wdind fnnapt fhm rajant îbhfks

lfsam `h nritari`h sat up`h tdair eraquahnias E`kk`wihb fra tda typas è

eiktars

at



Rdatdar `r h`t `lviùs ft tdis g`gaht Imafk Eik tars fra uhrafk izflka _rfntinfk

e ik tars fra masibham t` lrihb i t fs nk`sa fs p`ssilka t` tda imafk nfsa ]dùbd ùr

`ljantiva is t` masibh mibitfk e ik tars warsquokk labih witd fhfkysis è fhfk`b eik tars

Kat rsquos fhfkyza f k`w pfss e ik tar nirnuit wdind wa fra fkrafmy efgik ifr witd

Dara ]rfhsear Euhnti`h



Kat rsquos usa f sigpka GF]KFL n`ma lak`w t` pk`t B( jω) varsus rfmifh eraquahny ω

w7lt63 N763 gfbBjw76sqrt(6+(wN)Xlt)3 sagik`bx(wgfbBjw)3

xkflak(Eraquahny ih rfmsan ∜ k`b snfka)3 ykflak(Gfbhituma è UùtUih)3

titka(Gfbhituma Ndfrfntaristins è lfsin N k`w-pfss eiktar)3 brimGF]KFL



_dfsa asp`hsa

w7lt63N763pdfsaBjw7-ftfh(wN)64pi3sagik`bx(wpdfsaBjw)3

xkflak(Eraquahny ih rfmsan - k`b snfka)3

ykflak(_dfsa è UùtUih - mabraas)3

titka(_dfsa Ndfrfntaristins è lfsin N k`w-pfss eiktar)3 brim



îgikfrky D_EL_E amp LE nfh la prasahtam ]rfhsear euhnti`hs fra sigukftam

lak`w

D_E L_E LE



]da ]rfhsear Euhnti`h

It sdùkm la quita n kafr ly h`w tdft fs efr fs n`gputfti`hs fra n`hnarham it is

tda trfhsear euhnti`h wdind is nfknukftam avary t iga t` e ihm f e ik tar rsquos e raquahny

rasp`hsa G`ra`var trfhsear euhnti`hs fra h`t mapahmaht `h I_ `r _ è systags fhm tday n`gpkataky ndfrfntariza tda systags ih eraquahny m`gfih

]darae`ra t` fhfkyza fhm masibh f eiktar systag wa `hky haam its trfhsear

euhnti`h t` la ch`wh ]da ihput sibhfk is mirantky guktipkiam witd tda trfhsear

euhnti`h t` bat tda masiram eiktaram ùtput îbhfk _r`nassihb is fkk flùt

n`gputfti`hs wdatdar fhfk`b `r mibitfk eiktars `hky trfhsear euhnti`hs fra

fhfkyzam fhm masibham dara Dahnae`rtd `hky trfhsear euhnti`hs fra tfkcamflùt fhm h`t tdair nirnuit igpkagahtfti`hs

B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at



^` efr wfs tdis eiktar masibh0

Fk tdùbd wa n`gputam fhm sigukftam fkk cihm è eik tars s` efr f vary igp`rtfht

quasti`h sti kk ragfihs t` la fhswaram- Rfs tdis e ik tar masibh0 H` i t wfs h`t Qp t ik k

h`w wa nùkm `hky fhfkyza bivah nirnui ts fhm nfknukfta tdai r trfhsear euhnti`hs

_ranisaky wa nùkm h`t spaniey tda nutèe eraquahny lfhmwimtd fttahuft i`h atn

fnn`rmihb t` ùr wisdas Ra dfm t` fnnapt wdftavar ndfrfntaristins tda eiktars

dfm

Rdft is Masibh0

]da `tdar w`rm e`r masibh is syhtdasis ^` efr er`g f bivah nirnuittrfhsear

euhnt i`h i ts ndfrfntarist ins(rasuk t) wfs nfknukftam `r fhfkyzam Ih Masibh- er`g f

bivah ndfrfntaristins(rasukt) tda nirnuittrfhsear euhnti`h is syhtdasizam Ih masibh

`r syhtdasis ndfrfntaristins(rasukt) fra spanie iam fnn`rmihb t` ùr wisdas viz wa

nfh spaniey- lfhmwimtd è tda pfss lfhm st`p lfhm fttahuft i`h nutèe eraquahnyatn fhm tda n`rrasp`hmihb nirnui t `r trfhsear euhnt i`h is syhtdasizam t` sft isey fk k

ùr spanieinfti`hs

Ditdart` tda mieearahna latwaah fhfkysis fhm syhtdasis sdùkm la n`hspinuùs



Katrsquos labih witd Luttarw`rtd k`w pfss ndfrfntaristins

It sdùkm la h`tam tdft ùr masibh stfrts witd tda eihfk masiram rasukt dara it is tda

Luttarw`rtd k`w pfss eiktar ndfrfntaristin p`kyh`gifk Flt(w) is ch`wh fs tda

gfbhituma squfram euhnti`h wn is tda gtmL nutèe eraquahny

at



agaglarFlt(w) is h`t B(s) Itrsquos f k`hb wfy t` b` B(s) is tda eihfk fhswar è tda

masibh

Rdy h`t tfca f masibh axfgpka0

Axfgpka 6

Mariva tda trfhsear euhnt i`h e`r tda tdirm `rmar (c7gt ) Luttarw`rtd k`w-pfss e ik tar

witd h`rgfkizam nutèe eraquahny wn76rfmsan

E`r c7gt wn76rfmsan sulstitutihb slt7(jw)lt7-wlt

_`kas è tda fl`va euhnti`h fra six ih huglars fhm fra k`nftam ft



tdasa six p`kas kia `h tda nirnugearahna e tda nirnka witd rfmius wn76rfmsan fs

sd`wh ]da trfhsear euhnti`h is e`rgam ly kaet dfke pkfha p`kas sgt s= fhm s1

tdarae`ra B(s) is fs bivah lak`w

îhna wa dfva gftkfl ih dfhm wa nfh usa sygs fhm axpfhm tda sygl`kin

`ljant avfkuft`rs t` sigpkiey tda mah`gihft`r è B(s) Gftkfl n`ma is

axanutam lak`w



sygs s3 mah7(s+6lt-sqrt(gt)jlt)(s+6)(s+6lt+sqrt(gt)jlt)

mah 7

(s+6lt-6ltigtX(6lt))(s+6)(s+6lt+6ltigtX(6lt))

axpfhm(mah)

fhs 7sXgt+ltsXlt+lts+6

]darae`ra B(s) sigpk ieias t`

]da fl`va B(s) is tda masiram trfhsear euhnti`h e`r tdirm `rmar c7gt Luttarw`rtd k`w

pfss eiktar witd h`rgfkizam nutèe eraquahny wn76rfmsan



ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6

ûlstitut ihb s7jw3 Gftkfl n`ma is sigukftam lak`w



Ie wa nfh matargiha tda vfriùs vfkuas- f hellip fc fhm l tdah ùr syhtdasis è

trfhsear euhnti`h wikk la `var E`kk`wihb tda pr`namura è fl`va axfgpka

nàeeiniahts e`r c76 t` 1 ft h`rgfk izam eraquahny wn 76rfmsan fra tflukftam lak`w

Ufkuas è tda nàeein iahts fi e`r c76 t` 1



]da tflka wdind wa just sfw is e`r h`rgfkizam eraquahny wn76rfmsan]da trfhsear

euhnt i`h n`rrasp`hmihb t` fntufk nutèe eraquahny nfh la ltfiham er`g tda

rakfti`h bivah lak`w

E`r

wh`rg7 wn76rfmsan

]da masiram st`p lfhm fttahufti`hs nfh la nfknukftam ly pk`ttihb Flt(w) ih mL

wdind is 6k`b|Flt(w)| vs w e`r vfriùs vfkuas è c N`gputihb tdis ih Gftkfl wa

bat

AE



H`w wa fra rafmy e`r haxt axfgpka

Axfgpka lt

Qsihb tda fttahuft i`h nurvas fl`va mar iva tda trfhsear euhnt i`h è f Luttarw`rtd

k`w∜pfss fhfk`b ei ktar witd pfss lfhm lfhmwimtd è 1 rfmsan fhm fttahufti`h ih

tda st`p lfhm è ft kafst -gt2mL e`r eraquahnias kfrbar tdfh 61 rfmsan

Ra raear t` eibura fl`va fhm ft ω ωN761 17gt wa saa tdft tda vartinfk kiha ft tdis vfkua

nr`ssas tda c7= nurva ft fppr`xigftaky -gt2mL wdind sftiseias ùr raquiragaht

]darae`ra



Fetar eurtdar avfkufti`h

îgukftihb witd GF]KFL



Ndalysdav ]ypa-I Eik tars



Rdft flùt D_E L_ELE0

E`kk`wihb fra tda trfhse`rgs usam t` n`hvart k`w pfss eiktars t` `tdar typas ly

trfhse`rgihb tda n`gpkax vfriflka mdashsrsquo



Its tiga t` masibh f lfhm-pfss ei ktar

Axfgpka gt

N`gputa tda trfhsear euhnti`h e`r f tdirm-`rmar lfhm-pfss Luttarw`rtd eik tar witd

gtmL pfss-lfhm er`g gtCrfmsan t` =Crfmsan er`g f tdirm-`rmar k`w-pfssLuttarw`rtd eik tar witd h`rgfkizam nutè e eraquahny

Er`g tflkas ùtkiham lae`ra e`r wn76rfmsan wa bat B(s) fs lak`w

apkfnihb s ly

B(s)76(sXgt(wlt-w6)Xgt+gts(wlt-w6)Xgtw6wlt+gts(wlt-w6)Xgtw6XltwltXlt+6sXgt(wlt-

w6)Xgtw6XgtwltXgt+ltsXlt(wlt-w6)Xlt+=(wlt-w6)Xltw6wlt+ltsXlt(wlt-

w6)Xltw6XltwltXlt+lts(wlt-w6)+lts(wlt-w6)w6wlt+6)



Gund mieeinukt t` manipdar tdùbd itrsquos h`t tda nfsa witd GF]KFL _k`ttihb tda

trfhsear euhnt i`h ih GF]KFL



Mieearahna Latwaah fh Fhfk`b fhm Mibitfk Eiktar

Fhfk`b Eiktar Mibitfk Ei ktar

Fhfk`b e iktars fra nirnuitigpkagahtfti`hs witd rasist`rs

nfpfnit`rs ihmunt`rs atn

_r`brfgs kica GF]KFL t`batdar witd

n`gputar nfh `hky sigukfta fhfk`b

eiktars

Fhfk`b e iktars pr`nass fhfk`b s ibhfks

Fhfk`b Eiktar dfrmwfra nfh h`t m`

fhytdihb aksa tdfh ei ktarihb

Mibitfk eiktars fra n`gputfti`hfk pr`nass

igpkagahtam witd fkb`ritdgs

_r`brfgs k ica GF]KFL t`batdar witd

n`gputar nrafta mibitfk eik tars

Mibitfk eiktars pr`nass misnrata fhm

mibitfk sibhfks

Maminftam dfrmwfra ch`wh fs M^_

pr`nass`rs (ab ]I- ]G^gtltN526gt M^C)fra ginr`pr`nass`rs fhm nfh m` fkg`st

fkk n`gputfti`hfk w`rc `tdar tdfh

eiktarihb



Rdara is Mibitfk Eiktar0

Ra gfy ihtuitivaky uhmarstfhm tdft mibitfk systags fra misnratizam varsi`hs è

tdair fhfk`b nùhtarpfrt Ra fks` ch`w tdft tda r`ka wdind is tfcah ly Kfpkfna

trfhse`rgs ih fhfk`b systags tda sfga is tfcah ly Z trfhse`rg ih mibitfk m`gfih

]darae`ra t` gfca f mibitfk eiktar er`g fhfk`b eik tar wa just haam t` ndfhba tdatrfhsear euhnti`h er`g Kfpkfna m`gfih t` Z m`gfih ûnd f Ndfhba is ch`wh fs

Likihafr trfhse`rgfti`h

B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)

I g p uk s aI hv fr i f

h t

] r fh s e `r g f t i `

h

at

L i k i h a f r

] r f h s e ` r g f t i ` h



Likihafr trfhse`rgfti`h usas tda trfhse`rgfti`h

t` trfhse`rg tda kaet-dfke è tda s-pkfha iht` tda ihtari`r è tda uhit nirn ka ih tda z

-pkfha Ra wi kk misnuss `hky tda lik ihafr trfhse`rgfti`h ih tda prasaht n`htaxt

]s is tda sfgpkihb rfta wdind is ranipr`nfk è sfgpkihb eraquahny e s

Fhfk`b fhm Mibitfk Eraquahny



Ih fl`va axprassi`h wf is fhfk`b eraquahny fhm wm is mibi tfk eraquahny

Rfrpihb

]da e`kk`wihb Likihafr trfhse`rgfti`h is fks` usam

fhm

at



Igpuksa Ihvfrifht ]rfhse`rg

It is `ltfiham ly sfgpkihb tda igpuksa rasp`hsa è fhfk`b e iktar

d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i

F Fie D(s) 7 tdah D(z) 7

s - p 6- a z

tda gfppihb e`rgukf is

6 6

s - p 6- a z

∽

∖ ∖

]da D(s) nfh la lr`cah iht` pfrtifk erfnti`hs fhm igpuksa ihvfrifht gatd`m la

usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =

N`gputa tda trfhsear euhnti`h B(z) è f k`w-pfss mibitfk eiktar witd gtmL nutèe

e raquahny ft ltDz fhm fttahuft i`h è ft kafst 6mL e`r eraquahnias braftar tdfh

=Dz ]da sfgpkihb eraquahny e s is ltDz

Er`g tda pranamihb axfgpkas `h fhfk`b masibh wa nfh nfknukfta tdft tda

e`kk`wihb Bh(s) gaats tda masibh raquiragahts



Fetar eurtdar sigpkieinfti`h



Avfkuftihb tda Gftkfl N`ma

lz7S521 6gt=9 521W3 fz7S6 ∜66=lt9 =6lt2W3 SBz w]W7eraqz(lzfzltlt)3

sagik`bx(w]fls(Bz)) fxis(S6 6 6W) d`km `h3

titka(Mibitfk K`w-_fss Eiktar) xkflak(Eraquahny ih Dz) ykflak(Gfbhituma)brim



K`w pfss mibitfk II spanieinfti`hs nfh fks` la bivah fs

Rfrpam eraquahnias fra bivah ly

Dara mdashirsquo is fhy sulsnript

E`r Luttarw`rtd Eiktars tda `rmar H fhm nutèe eraquahny Ωn nfh la rakftam t` fl`va

spanieinfti`hs fs e`kk`ws



Baharfk trfhsear euhnti`h B(s) e`r fhy p`kyh`gifk euhnti`h nfh la writtah fs

Luttarw`rtd nàeeiniahts fra bivah ly

F is tda bfih e B(s) wdind is 76 e`r pfssiva eiktars

E`r Ndalysdav Eiktars tda `rmar H fhm nutèe eraquahny Ωn nfh la rakftam t` tda eiktar



E`r Ndalysdav Eiktars tda `rmar H fhm nutèe eraquahny n nfh la rakftam t` tda eiktar

spanieinfti`hs spanieinfti`hs fs e`kk`ws

Ndalysdav nàeeiniahts fra bivah ly




Rdara fra wa0

bullRa gust p`hmar h`w wdft is ùr nurraht stftus è kafrhihb mibitfk eik tar

bull Fra wa m`ha witd it0 Ie h`t tdah wdft aksa sdùkm la kafrht t` n`gpkatait

bull Rdft fra tda p`ssilka nkfssieinfti`hs è mibitfk eiktar masibh

bullRa ch`w d`w t` `ltfih mibitfk eiktar er`g fhfk`b masibh usihb likihafrtrfhse`rg

bullRa haam t` ch`w wdft fra EI fhm II eik tars

bull Ra haam t` ch`w tdft ie mibitfk ei ktars fra lr`fmky nftab`rizam uhmar IIfhm EI tdah uhmar wdind nftab`ry wùkm lik ihafr trfhse`rg efkk fhm wdy0

at

Mi it k Eikt M i



Mibitfk Eiktar Masibh

Eraquahny

sfgpkihb

gatd`m

II Masibh

]rfhsiaht ]iga M`gfih Fppr`fnd ^pantrfk Eraquahny M`gfih Fppr`fnd

Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e

Billrsquossnikkfti`hs

Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga

Rdy is Likihafr trfhse`rg fss`niftam witd spantrfk fppr`fnd0

Ih ùr stumy s` efr wdatdar fhfk`b `r mibi tfk wa fhfkyzam fhm syhtdasizam

trfhsear euhnti`hs `hky wdind fra eraquahnyspantrfk m`gfih qufhtitias

]darae`ra h`t just likihafr trfhse`rgfti`h lut ùr ahtira stumy s` efr dfm laaheraquahny m`gfih stumy

Rdy is EI fss`niftam witd spantrfk fppr`fnd0

Er`g sibhfks fhm systags wa ch`w tdft tda qufhtity wdind is ch`wh fs

trfhsear euhnti`h ih eraquahny m`gfih is ch`wh fs igpuksa rasp`hsa ih tiga

m`gfih



]darae`ra f masibh wdind syhtdasizas igpuksa rasp`hsa ihstafm è trfhsear

euhnti`h is fss`niftam witd trfhsiahttiga-m`gfih masibh fhm Eihita igpuksa

rasp`hsa (EI) is `ha è td`sa

Rdft is Eihita flùt EI0

]` axpkfih tdis kat us k``c ft tda igpuksa rasp`hsa è fh imafk eik tar

]rfhsear Euhnti`h Igpuksa asp`hsa

Eraquahny M`gfih ]iga M`gfih



Ra nfh `lsarva tdft tda igpuksa rasp`hsa è fh imafk eiktar is ihmaam iheihita fhm

is tdarae`ra h`h-nfusfk îhna h`h-nfusfk igpuksa rasp`hsa nfh h`t la prfntinfkky

igpkagahtam ih tiga m`gfih tdarae`ra it is truhnftam fhm gfma eihita (EI) fhm

tdft is e ih ita flùt EI

Ie II is t` t iga m`gfih tdah wdy is i t tfbbam ih eraquahny m`gfih0

Ra nùkm saa tdft II is h`t p`ssilka t` igpkagaht ih tiga m`gfih lanfusa è its

h`h-nfusfk hftura h tda `tdar dfhm ih eraquahny m`gfih fppr`fnd sihna wa m`

h`t mafk witd igpuksa rasp`hsa tdarae`ra wa havar truhnfta it fs f rasukt fkktrfhsear euhnti`hs ih eraquahny m`gfih fppr`fnd rasukt ih iheihita igpuksa

rasp`hsa (II) ]dis gafhs tdft II masibh is t` eraquahny m`gfih fppr`fnd

Katrsquos fbfih dfva f k``c ft tda mieearaht nftab`rias typas fhm stfbas è mibitfk eiktarmasibh t` uhmarstfhm tdag lattar





Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Eihita Igpuksa asp`hsa (EI) Eiktar Masibh

Rdftavar eiktar masibh wa mim tikk h`w wfs II masibh wdara wa mim h`t truhnfta

tda igpuksa rasp`hsa lut h`w it is turh t` stumy EI masibh wdind is f tiga

m`gfih fppr`fnd fhm tdus it truhnftas tda igpuksa rasp`hsa

Rdy EI0

]` fhswar tdis katrsquos n`gpfra pr`s fhm n`hs è l`td tda masibhs

EI Bivas Kihafr pdfsa rasp`hsa wi td

ih tda pfss lfhm

EI dfs g`ra huglar è sima k`las ih

st`p lfhm tdfh II

EI dfs g`ra n`gputfti`hfkn`gpkaxity fhm ahbfbas g`ra

gag`ry

II dfs g`stky h`h k ihafr pdfsa

rasp`hsa

II dfs gund kassar huglar è sima

k`las ih tda st`p lfhm

II dfs kassar n`gputfti`hfk

n`gpkaxity fhm ahbfbas kassar

gag`ry

Eihita Igpuksa asp`hsa (EI) Iheihita Igpuksa asp`hsa (II)

at

Eùriar ]rfhse`rg Gatd`m



Fs wa nùkm saa tdft fkk imafk ei ktars tfca tda sdfpa è f bfta euhnti`h ih

eraquahny m`gfih tdarae`ra tday fra sfgpkihb euhnti`h ih t iga m`gfih (er`g

Eùriar trfhse`rg) ]da igpuksa rasp`hsa dahna is f sfgpk ihb euhnti`h fhm is

II ih hftura II gfcas tda trfhsear euhnti`h h`h nfusfk tdarae`ra e`kk`wihb

staps fra tfcah t` gfca tda igpuksa rasp`hsa fhm trfhsear euhnti`h nfusfk

6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa

asp`hsa (H`h-Nfusfk)

Eihita Igpuksa asp`hsa

(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at

Er`g Eùriar trfhse`rg è bfta euhnti`hs fhm sulsaquaht truhnfti`h è igpuksa



rasp`hsas e`kk`wihb tflka is gfma t` `ltfih igpuksa rasp`hsas è mieearaht typa

è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦

jω jωh6d(h) 7 D(a )a m

lt

Ϗ

Ϗ

ω

Ϗ ∜∣

jω jωh6d( ) D( ) m

Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt

a 7 a (pfsslfhm)e`r D(z) 7 D(a )

(st`plfhm)d(h)is rapkfnam ly d(h -ύ)

e`r axfgpka d(h) e`r k`wpfss typa ih fl`va tflka lan`gas

Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)

dara is tda pdfsa makfy r brùp makfy e tda systag ia( )

m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1

Nfknukfta tda eik tar nàeeiniahts e`r f gt-tfp EI k`w-pfss eiktar witd f nutèe

eraquahny è 4 Dz fhm f sfgpkihb rfta è 4 Dz usihb tda Eùriar

trfhse`rg gatd`m

sfgpka



_k`ttihb D(z) ih GF]KFL wa bat tda e`kk`wihb




Axfgpka 5



p

Nfknukfta tda eik tar nàeeiniahts e`r f 62-tfp EI k`w-pfss eik tar witd f nutèe

e raquahny è 4 Dz fhm f sfgpk ihb rfta è 4 Dz usihb tda Eùr iar

trfhse`rg gatd`m

62 tfp EI k`w pfss nàeeiniahts fra nfknukftam fhm D(z) _D(z) fra pk`ttam lak`w

Axfgpka 2



p

Nfknukfta tda ei ktar nàeein iahts e`r f 1-tfp EI lfhm-pfss eik tar witd f

k`war nutèe eraquahny è lt Dz fhm fh uppar nutèe e raquahny è

lt= Dz ft f sfgpk ihb rfta è 4 Dz



k tti D( ) i td GF]KFL t



h pk`ttihb D(z) wi td GF]KFL wa bat

Rdft fra tda pr`lkags ih EI masibh witd Eùriar ]rfhse`rg Gatd`m0



b

bull ]da pfss lfhm gfbhituma rasp`hsas fra quita lak`w mL kavak

bull]dara fra uhmasirflka rippkas ih pfss lfhm fs wakk fs st`p lfhm

bull ]dara fra t`` gfhy sima k`las wd`sa gfbhitumas fra n`gpfrflka t` gfih k`la

wdind nfh rahmar fhy eiktar ihaeeantiva

Fk k tda fl`va pr`lkags fra fttrilutam t` f pdah`gah`h nfkkam Billrsquos Aeeant `r

Billrsquos sni kkfti`hs ]dasa sni kkfti`hs `nnur mua t` tda flrupt truhnfti`h è

igpuksa rasp`hsa wdind is fh ihdaraht pr`lkag è EI masibh

Rdft is tda ^`kuti`h0

F wihm`w euhnti`h wdind is syggatrinfk fhm nfh brfmufkky waibdt tda masibham

EI nàeeiniahts m`wh t` zar`s ft l`td ahms e`r tda rfhba è G ≭ h equiv G

Rihm`w Gatd`m



Ih tdis santi`h tda wihm`w gatd`m (Eùriar trfhse`rg masibh witd wihm`w

euhnti`hs) is mavak`pam t` ragamy tda uhmasirflka Bills `snik kft i`hs ih tda pfss-

lfhm fhm st`p-lfhm è tda masibham EI eiktar anfkk tdft Bills `snikkfti`hs

`ribihfta er`g tda flrupt truhnft i`h è tda ihe ih ita-kahbtd nàeeiniaht saquahna

]dah it is hfturfk t` saac f wihm`w euhnti`h wdind is syggatrinfk fhm nfhbrfmufk ky waibdt tda masibham EI nàeeiniahts m`wh t` zar`s ft l`td ahms e`r tda

rfhba è G ≭h equiv G Fppkyihb tda wihm`w saquahna t` tda eik tar nàeeiniahts bivas

at

N`gpfrftiva sdfpas è Mieearaht Rihm`ws



p p

^taps ih Rihm`w Masibh




Axfgpka 4

Masibh f 1-tfp EI lfhm rajant ei ktar witd f k`war nutè e e raquahny è lt Dz fh

uppar nutèe eraquahny è lt= Dz fhm f sfgpkihb rfta è 4 Dz usihb tdaDfggihb wihm`w gatd`m





Axfgpka 46



F k`w pfss eiktar is t` la mas ibham witd e`kk`wihb masiram e raquahny rasp`hsa j -jlt

jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭

Matargiha tda eiktar nàeeiniahts d(h) ie w ihm`w euhnt i`h is maeiham fs

6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=

jω jωh -jltω jωh

=

Aitdar ly avfkuftihb tda e`kk`wihb ihtabrfk r er`g tda tflkas

6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω

nuktfi`h e d(h) 7 d(h) (h) er`g fl`va

tda eraquahny rasp`hsa is nfknuktam usihb e`kk`wihb axprassi`h

D(a ) 7 d(h) a

fetar avfkufti`h

6 lt 6D(a ) 7 a n`s n`s lt

=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



Masibh f k`w-pfss EI eiktar witd lt1 tfps usihb mdashe irwmrsquo ]da nutèe eraquahny è

tda eik tar is lt Dz fssugihb f sfgpk ihb eraquahny è 4 Dz ^d`w

n`gpfrftiva eraquahny fhm pdfsa rasp`hsas è tda eik tar usihb rantfhbukfr

Dfggihb Dfhhihb fhm Lkfncgfh Rihm`w euhnti`hs

Ritd f bivah sfgpk ihb rfta e 4 Dz tda h`rgfkizam nutèe eraquahnynfh la eùhm fs

H`w wa fra rafmy t` masibh EI eiktars vif tda GF]KFL pr`brfg-eirwm ]da pr`brfg

eirwm(HEtypaRhKRhDRtypa) dfs eiva ihput pfrfgatars wdind fra masnrilam fs e`kk`ws

bull mdash mdashHrsquorsquo is tda huglar è spanie iam eik tar nàeeiniahts (tda huglar è e ik tar tfps)

bull mdashmdashEtyparsquorsquo mah`tas tda e ik tar typa tdft is ihput mdashmdash6rsquorsquo e`r tda k`w-pfss e ik tar masibh ihput mdashmdashltrsquorsquo e`r

tda dibd-pfss eik tar masibh ihput mdashmdashgtrsquorsquo e`r tda lfhm-pfss eik tar masibh fhm ihput mdashmdash=rsquorsquo e`r tda

lfhm rajant ei ktar masibh

bull RhKrsquorsquo fhm mdashmdashRhDrsquorsquo fra tda k`war fhm uppar nutè e e raquahny ihputs raspant ivaky H`ta tdftRhD 7 wdah spani eyihb RhK e`r tda k`w-pfss ei ktar masibh wdi ka RhK 7 wdah spani eyihb

RhD e`r tda dibd-pfss eik tar masibh

bull mdashmdashRtyparsquorsquo spanie ias tda wihm`w mftf saquahna t` la usam ih tda masibh tdft is ihput mdashmdash6rsquorsquo e`r

tda rantfhbukfr wihm`w ihput mdashmdashltrsquorsquo e`r tda trifhbukfr wihm`w ihput mdashmdashgtrsquorsquo e`r tda Dfhhihb

wihm`w ihput mdash mdash=rsquo rsquo e`r tda Dfggihb wihm`w fhm ihput mdashmdash1rsquorsquo e`r tda Lkfncgfh

wihm`w

asukt fetar axanuti`h è n`ma e`r axfgpka 9 sd`ws tda e`kk`wihb ùtput



E`r f n`ggarnifk masibh nartfih agpirinfk rasukts fra hanassfry wdind fra



tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p

Masibh f lfhm-pfss EI eiktar witd tda e`kk`wihb spanieinfti`hs

6)K`war st`p-lfhm 7 bdquo1 Dz lt)_fsslfhm 7 65bdquoltgt Dz gt)Qppar st`p-lfhm 7

gt1bdquo= Dz =)^t`plfhm fttahufti`h 7 1 mL 1)_fsslfhm rippka71 mL

5)^fgpkihb rfta 7 4 Dz

GF]KFL pr`brfg bivas tda e`kkìhb ùtput



p b b b p

Cfisar Rihm`w



^` efr ndìna è tda wihm`w euhnti`h fhm tda vfkua è G fra tda `hky tw` eraam`gs

tdft wa dfm e`r n`htr`kk ihb tda trfhsi ti`h lfhmwimtd ω lut tda gihigug st`p-

lfhm fttahufti`h mapahms `hky `h tda wihm`w euhnti`h wa nd``sa fhm h`t tda

vfkua è G Cfisar wihm`w euhnti`h pr`vima n`htr`k `var l`td νs fhm tda wimtd è

tda trfhsiti`h lfhmwimtd emptyω Fmmiti`hfk pfrfgatars ζ fhm μ pr`vima tdis

fmmiti`hfk n`htr`k ]da Cfisar wihm`w is maeiham ly

wdara I sup2 is tda g`mieiam zar`-`rmar Lassak euhnt i`h It is f p`war sarias è tdae`rg



e`rg

Ra n`gputa tda vfkuas è tda Cfisar wihm`w euhnti`h ih tdraa staps fs e`kk`ws

bull ]da pfrfgatar μ raquiram t` fndiava tda masiram fttahufti`h ζ s 7 ∜lt k`b6(ν s )

ih tda st`p-lfhm is nfknukftam er`g tda e`kk`wihb agpirinfk e`rgukf marivam ly

Cfisar (tda rippka ih tda pfss-lfhm is hafrky tda sfga fs ν s )

bull Haxt tda `rmar è tda eiktar H (7ltG) is astigftam er`g fh`tdar agpirinfk e`rgukf

marivam ly Cfisar

bull ]da tdirm stap is t` n`gputa Ix Ih prfntina fmmihb f eihita huglar è targs

sfy lt targs è tda iheihita sarias bivas f sueeiniahtky fnnurfta vfkua e`r Ix

Axfgpka 66

M i EI k _ Eikt i C i i m itd m e td eikt H =1



Masibh è tda K_ Eiktar usihb tda Cfisar wihm`w

]da kahbtd è Cfisar wihm`w gust la `ha dibdar tdfh tda

`rmar(H7=1) è tda EI eiktar `ltfiham er`g tda euhnti`h Cfisar`rm

l7eir6(=1 gt1 cfisar(=5 gtgt91gt))3 SdwW7eraqz(l6lt15)3

Dml7ltk`b6(fls(d))3 pk`t(wpiDgtml)3

titka(Gfbhituma è K_ witd H7=1 fhm Cfisar wihm`w)

ykflak(Gfbhituma ih mL)

xkflak(H`rgfkizam eraquahny)

Masibh fh EI k`w _fss Eiktar usihb Cfisar wihm`w witd `rmar è tda eiktar H7=1

witd nutèe eraquahny ωn7gt1 rfmifhssfgpka3μ7gtgt91gt

ptigfk Eiktar Masibh



]da ptigfk Ei ktar masibh igpkagahts _frcs-GnNkak kfh fkb`ri tdg ]dis is lfsam

`h gihigizihb tda gfxigug fppr`xigfti`h arr`r ih f Ndalysdav p`kyh`gifk

Bivah fh imafk eraquahny rasp`hsa Dm(a jω]) tda fppr`xigfti`h arr`r A(ω) is

maeiham fs

wdara D(a jω]) is tda eraquahny rasp`hsa è tda kihafr pdfsa EI eiktar t` la

masibham fhm R(ω) is tda waibdt euhnti`h e`r agpdfsizihb nartfih eraquahny

lfhms `var `tdars murihb tda `ptigizfti`h pr`nass ]dis pr`nass is masibham t`

gihigiza tda arr`r sd`wh fl`va ]da eibura lak`w eurtdar nkfrieias tda n`hnapt

fhm sd`ws tda mie earaht h`tft i`h usam ih tda masibh pr`nass

Gfbhituma asp`hsa è f _rfntinfk(Ndalysdav)

K`w-pfss fhm imafk K`w pfss n`gpfram

Arr`r latwaah imafk fhm prfntinfk asp`hsa

Raibdtam arr`r is fks` sd`wh





Axfgpka 6lt

Masibh f k`w-pfss ei ktar witd tda e`kk`wihb spanieinfti`hs

M^_ systag sfgpkihb rfta 7 4 Dz3 _fss-lfhm 7 bdquo4 Dz3 ^t`p-lfhm 76bdquo

= Dz3 _fss-lfhm rippka 7 6 mL3 ^t`p-lfhm fttahufti`h 7 = mL3 Eiktar `rmar 71gt

]dah fppkyihb Aqufti`h stftam fl`va bivas



Fpfrt er`g tda pk`t tda eiktar nàeein iahts tdus avfkuftam fra fks` tflukftam ih tda

haxt tflka ]da gfbhituma fhm pdfsa rasp`hsas fra fks` pk`ttam nartfihky tda eik tar

rasp`hsa n`he`rgs witd tda `ptigizfti`h raquiragahts

]da Gftkfl pr`brfg e`r axfgpka 6lt is writ tah lak`w3

EI eiktar nàeeiniahts ih Axfgpka 6lt





Eraquahny ^fgpkihb Gatd`m

6 Ih tdis gatd`m masiram gfbhitumas è tda eraquahny rasp`hsa is mirantky



6Ih tdis gatd`m masiram gfbhitumas è tda eraquahny rasp`hsa is mirantky

gahti`ham ft eraquahny pìhts matargiham er`g h` è tfps raquiram ih tda

masibh

lt]` tda mirantky spanie iam gfbhitumas ih eraquahny m`gfih IME] is fppk iam t` battda n`rrasp`hmihb igpuksa rasp`hsa

gt]da igpuksa rasp`hsa pr`vimas tda raquiram nàeeiniahts è tda trfhsear

euhnti`hs viz ll6helliplH-6

= ]da trfhsear euhnti`h is e ihfk ky pk`ttam fbfihst eraquahny

ll6helliplH-6D(z) 7 l+l6z-6+lH-6z

-(H-6)Masibham Eiktar

Imafk Ndfrfntaristins^fgpkam gfbhitumas spanieiam

er`g h` è tfps Eihita Igpuksa

asp`hsaIME]

at

]da _r`namura is suggfrizam lak`w



6 Bivah tda eiktar kahbtd è ltG + 6 spani ey tda gfbhituma eraquahny rasp`hsa e`r

tda h`rgfkizam eraquahny rfhba er`g t` Ϗ

lt Nfknukfta EI eiktar nàeeiniahts

gt Qsa tda syggatry (kihafr pdfsa raquiragaht) t` matargiha tda rast è tda

nàeeiniahts

= ltfih tda trfhsear euhnti`h nàeeiniahts viz ll6helliplH-6 er`g igpuksa rasp`hsa

fhm n`gpkata tda masibh

Axfgpka 66

Masibh f kihafr pdfsa k`w-pfss EI eiktar witd 2 tfps fhm f nutè e eraquahny è U 7



Masibh f kihafr pdfsa k`w-pfss EI eiktar witd 2 tfps fhm f nutè e e raquahny è Un 7

gtϏ rfmifhsfgpka usihb tda eraquahny sfgpkihb gatd`m



Billrsquos snikkfti`hs ihtr`munas rippkas

Axfgpka 6lt

Masibh f kihafr pdfsa k`w-pfss EI eiktar witd lt1 nàeeiniahts usihb tda eraquahny




sfgpkihb gatd`m Kat tda nutèe eraquahny la lt Dz fhm fssuga f sfgpk ihb

eraquahny è 4 Dz

]da gfbhituma eraquahny rasp`hsa pk`ttam usihb tda mfsd-m`ttam kiha ismispkfyam ih tda upn`gihb eibura wdara i t is `lsarvam tdft `snikkfti`hs (sd`wh

fs tda mfsd-m`ttam k iha) `nnur ih tda pfss-lfhm fhm st`p-lfhm è tda masibham

EI eiktar ]dis is mua t` tda flrupt ndfhba è tda spanieinfti`h ih tda trfhsiti`h

lfhm (latwaah tda pfss-lfhm fhm tda st`p-lfhm) ]` ramuna tdis rippka ae eant

tda g`mieiam spanieinfti`h witd f sg``td trfhsiti`h lfhm Dc c 7 6 6gt is

usam

]` efniki tfta afsy n`gputfti`h fh`tdar GF]KFL euhnti`h mdash eires rsquo is writtah e`r

eraquahny sfgpkihb gatd`m masibh E`kk`wihb fra tda spanieinfti`hs




Ra wikk usa tdarsquo e ires rsquo euhnti`h t` masibh tda e ik tar è axfgpka 6lt dara tda pr`brfg

s writ tah wdind avfkuftas tda masibh witd fh flrupt gfbhi tuma spanie inft i`h fhm

fh`tdar witd sg``td gfbhituma spanie infti`hs s` tdft Bills pdah`gah`h nfh la

afsiky varieiam

Brfpd `ltfiham er`g GF]KFL pr`brfg is bivah lak`w





EIK]A AFKIZF]IH

Mirant-E`rg I afkizfti`h



Fs wa ch`w f mibitfk e iktar trfhsear euhnti`h D(z) is bivah ly

Kat x(h) fhm y(h) la tda mibi tfk eik tar ihput fhm ùtput raspantivaky Ra nfh axprass

tda rakfti`hsdip ih z-trfhse`rg m`gfih fs

Y(z) 7 D(z)T(z)

wdara T(z) fhm Y(z) fra tda z-trfhse`rgs è x(h) fhm y(h) raspantivaky Ie wa

ûlstituta fl`va Aqufti`h iht` D(z) ih prasaht aqufti`h wa dfva

]fcihb ihvarsa Z trfhse`rgs

]dis mieearahna aqufti`h tdus nfh la igpkagahtam ly f mirant-e`rg I rafkizfti`hsd`wh ih Eibura(F) pfrt (L) pfrt ik kustrftas tda rafkizfti`h è tda san`hm-`rmar II

eik t (G H lt) H t td t td t ti m i Ei (N) t



eik tar (G 7 H 7 lt) H`ta tdft tda h`tfti`h usam ih Eiburas(N) pfrt

Mirant-E`rg II afkizfti`h



N`hsimarihb Aqufti`hs ih pranamihb pfrfbrfpd witd H 7 G wa nfh axprass

Rdara

]dah wa bat

]da mie earahna aqufti`hs fra tdus

]dis mieearahna aqufti`h tdus nfh la igpkagahtam ly f mirant-e`rg II rafkizfti`hsd`wh ih Eibura(F) pfrt (L) pfrt ik kustrftas tda rafkizfti`h è tda san`hm-`rmar II

ei ktar (G 7 H 7 lt)




Nfsnfma (ârias) afkizfti`h

Fh fktarhfta wfy t` e iktar rafkizfti`h is t` nfsnfma tda efnt`rizam D(z) ih tdae`kk`wihb e`rg

D(z) 7 D6(z)Dlt(z)hellipDc(z)

wdara Dc(z) is nd`sah t` la tda eirst- `r san`hm-`rmar trfhsear euhnti`h (santi`h)

wdind is maeiham ly



E`r Axfgpka

_frfkkak afkizfti`hH`w wa n`hvart D(z) iht` tda e`kk`wihb e`rg



Axfgpka -6gtBivah f san`hm-`rmar trfhsear euhnti`h

_are`rg tda eik tar rafkizfti`hs fhm writa tda mieearahna aqufti`hs usihb tda

e`kk`wihb rafkizfti`hs6 mirant e`rg I fhm mirant e`rg II

lt nfsnfma e`rg vif tda eirs t-`rmar santi`hs

gt pfrfkkak e`rg vif tda eirst-`rmar santi`hs



Mirant e`rg I Mirant e`rg I

]da mie earahna aqufti`hs e`r tda mirant-e`rg II rafkizfti`h fra axprassam fs



]` fndiava tda nfsnfma (sarias) e`rg rafkizfti`h wa efnt`r D(z) iht` tw` eirst -`rmar

santi`hs t` yiakm

Nfsnfma E`rg

Ih `rmar t` yiakm tda pfrfkkak e`rg è rafkizfti`h wa haam t` gfca usa è tda pfrtifkerfnti`h axpfhsi`h fhm wikk ei rst kat



Qsihb Mirant e`rg II t` baharfta mieearahna aqufti`hs e`r afnd santi`h



_frfkkak E`rg

Axfgpka 6=Qsa GF]KFL t` rafkiza tda e`kk`wihb trfhsear euhnt i`h ih Mirant E`rg-II



Mirant E`rg-II rafkizfti`h è D(z) usihb GF]KFL îgukihc

Ihput amp utput îbhfks è tda ^ystag er`g ^n`pa



GQK]I-F]A

MIBI]FK ÎBHFK _NA^ÎHB

GQK]I-F]A M^_



Ih gfhy frafs è mibitfk sibhfk pr`nassihb (M^_) fppkinfti`hsrdquosund fs

n`gguhinfti`hs spaand fhm fumi` pr`nassihbrdquorisihb `r k`warihb è f sfgpkihbrfta is raquiram ]da prihnipka tdft mafks witd ndfhbihb tda sfgpkihb rfta lak`hbs

assahtifk ky t` guktirfta sibhfk pr`nassihb (Ieafnd`r fhm Jarvis ltlt3 _`rft69923

_r`fcis fhm Gfh`kfcis 69953 ^`rahsah fhm Ndah 6992) Fs fh ihtr`munti`h wa

wikk e`nus `h sfgpkihb rfta n`hvarsi`h3 tdft is sfgpkihb rfta ramunti`h `r

ihnrafsa

]da pr`nass è ramunihb f sfgpkihb rfta ly fh ihtabar efnt`r is raearram t` fs

m`wh sfgpkihb è f mftf saquahna Ra fks` raear t` m`wh sfgpkihb fs

mdashmdashman igfti`hrsquorsquo(h`t tfcihb `ha è tah) ]da targ mdashmdashmanigfti`hrsquorsquo usam e`r tda m`wh

sfgpkihb pr`nass dfs laah fnnaptam fhm usam ih gfhy taxtl``cs fhm eiakms

M`wh sfgpkihb f mftf saquahna x(h) is usufkky m`ha ly fh ihtabar efnt`r è

M(manigfti`h)îgikfrky ihnrafsihb tda sfgpkihb rfta is up sfgpkihb `r mdashihtarp`kfti`hrsquo è x(h) ly f ihtabar efnt`r I(ihtarp`kfti`h)



Kihafr Eiktar ndfrfntaristins

^fgpkihb rfta è f sibhfk nfh la ndfhbam usihb tda fl`va kihafr eik tar

-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)

d(h)is rapkfnamlyd(h -ύ)

Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣



Manigfti`h ly f efnt`r M





]da aeeant `h spantrug lae`ra fhm fetar manigfti`h



Ihtarp`kfti`h ly f efnt`r I











îbhfk Ek`w Brfpds fhm Lk`nc mifbrfg aprasahtfti`h

M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M

s(h) 6 h7 paraGltGhellip

`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)

Guktistfba Igpkagahtfti`hs



Guktistfba Ihtarp`kft`rs

Guktistfba Manigft`rs

ippka fhm EI eik tar kahbtd(G) rakfti`h



_`kypdfsa Man`gp`sit i`h è Eiktar trunturas∘

∖ -h -6 -lt -gtD(z) 7 d(h)z 7 d()+d(6)z +d(lt)z +d(gt)z +



h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G

tdafl`va axprassi hnfh la man`gp`sam iht`

D(z) 7 d()+d(G)z +d(ltG)z +d(gtG)z +

+ z d(6)+d(G+6)z +d(ltG+6)z +d(gtG+6)z +

+ z d(lt)+d(G+lt)z +

∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt

d(ltG+ lt)z +d(gtG+ lt)z +

+ z d(G-6)+d(ltG-6)z +d(gtG-6)z +d(=G-6)+

n`hmahsihb tda fl`va aqufti`h iht`

D(z) 7 d(gG+c)z 7 z d(gG+c)z

7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )

Rdara A (z ) 7D(z) e`r c 7 i 7 6ltG-6

gftrixraprasahtfti`h

A (z )

A (z )

D(z) 7 6z z

A (z )

^trunturfk Lk`nc aprasahtfti`h



Mirant e`rg

_`kypdfsa e`rg



^truntura N`gpfris`h



E`km Mirant e`rg gt E`km _`kypdfsa e`rg



]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta





]dis aqufti`h è strfibdt kiha witd s k`pa -ltcmLmanfma

A]



NH]AH]^

6 Eiktars fra Imafkky Kihafr ]iga Ihvfrifht systagslt Rdft fra Eiktars0

gt ]da ]rfhsear Euhnti`h

= Katrsquos labih w itd Lut tarw`rtd k`w pfss ndfrfntaristins

1 Rdara is Mibitfk Eiktar (Lik ihafr ]rfhse`rg)0

5 Rfrpihb

2 Rdara fra wa04 Mibitfk eiktar Masibh Ek`w Mifbrfg

9 Eihita Igpuksa asp`hsa (EI) Eiktar Masibh

6Eùriar ]rfhse`rg Gatd`m

66Rihm`w Gatd`m

6ltEraquahny ^fgpkihb Gatd`m




at



Rdft fra Eiktars0



eiktars

at
















_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

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Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

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Ihtr`muna

makfy t`

gfca

nfusfk

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rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

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t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

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]ruhnfti`h

è II t`gfca EI

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trfhse`rg

gatd`m

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at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




at



Rdft fra Eiktars0



eiktars

at
















_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

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U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

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pkfnagaht

masibh

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ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

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t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

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Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

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rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

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Masibh

K`w pfss

pr`t`typa

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Masibh

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è II t`gfca EI

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trfhse`rg

gatd`m

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at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

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ω ω

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Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







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p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

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(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Rdft fra Eiktars0



eiktars

at
















_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

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ih

ih ùt

UB(s)3

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at









dfm

Rdft is Masibh0






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at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

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E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












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d(h)7 df(h]s)

i s

i s

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p ] -6i76 i76i

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6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

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+ + + +7 ∜

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Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

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makfy t`

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Rihm`w

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pkfnagaht

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ihvfrifht

masibh

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trfhse`rg

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Masibh

K`w pfss

pr`t`typa

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t` tdar

typas

Rfrpihb

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euhnti`h

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Eùriar

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at



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m`gfih


























Eraquahny

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gfca

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rasp`hsa

Rihm`w

gatd`m

EI Masibh

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pkfnagaht

masibh

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ihvfrifht

masibh

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Masibh

K`w pfss

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è II t`gfca EI

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at







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ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


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gag`ry


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6

1

=

gt

ltImafk ei ktar

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(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

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Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

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ω

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-G (h -ύ) G)


m m( )

pdfsa makfy

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ύ

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ω ω

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trfhse`rg gatd`m

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p



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p













b











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at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

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6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

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d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

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w

= jω -jωh

w

h7

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D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

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wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



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Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

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x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]
















_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

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ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

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Masibh

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Masibh

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è II t`gfca EI

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trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























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gatd`m

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gfca

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rasp`hsa

Rihm`w

gatd`m

EI Masibh

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pkfnagaht

masibh

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ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

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ag`vfk e


Eùriar

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gatd`m

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at







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ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

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(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







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p



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p













b











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at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

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6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

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w

= jω -jωh

w

h7

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fetar avfkufti`h


=

ω

ω ω

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+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

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ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

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]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



_dfsa asp`hsa








lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




lak`w

D_E L_E LE












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












B(s)

s 7 jw

UùtUih

7ùt

ih

ih ùt

UB(s)3

U

U B(s) 7 U

at









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









dfm

Rdft is Masibh0






ùr spanieinfti`hs








at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







at




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




masibh


Axfgpka 6












axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








axanutam lak`w




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




mah 7


axpfhm(mah)







ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



ω

ω ω ω gt lt

6B(j ) 7

-j - lt + ltj +6













E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






E`r

wh`rg7 wn76rfmsan



bat

AE




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Axfgpka lt






]darae`ra
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]
















Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Axfgpka gt




apkfnihb s ly
















eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]













eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









eiktars









mibitfk sibhfks




eiktarihb









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









B(s)Uùt(s)Uih(s)

B(z)Uih(z) Uùt(z)


h t


h

at

L i k i h a f r












Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]











Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Rfrpihb


fhm

at





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





d(h)7 df(h]s)

i s

i s

G Gi i

p ] -6i76 i76i

p ] -6i


s - p 6- a z


6 6

s - p 6- a z

∽

∖ ∖


usam e`r axfgpka

6 lt 6

6

6 lt

6 6 6( )

( 6)( lt) ( 6) ( lt)6 6

( )(6 ) (6 )

ltgtlt5( )

6 1gtlt =94

] ]

Ie D s

s s s s

tdahD za z a z

z D z

z z

∜ ∜ ∜ ∜

∜

∜ ∜

7 7 ∜

+ + + +7 ∜

∜ ∜

7∜ +



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Axfgpka =




































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]































Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




























Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






















Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]















Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Rdara fra wa0







at

Mi it k Eikt M i




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Fhswar Ga








m`gfih


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]


























Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]

















Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Eraquahny

sfgpkihb

gatd`m

II Masibh


Ihtr`muna

makfy t`

gfca

nfusfk

igpuksa

rasp`hsa

Rihm`w

gatd`m

EI Masibh

_`ka-zar`

pkfnagaht

masibh

Igpuksa

ihvfrifht

masibh

Likihafr

trfhse`rg

fti`h

Fhfk`b

Masibh

K`w pfss

pr`t`typa

]rfhse`rg

t` tdar

typas

Rfrpihb

Likihafr

trfhse`rgfti`h

Rihm`w

euhnti`h

ag`vfk e


Eùriar

trfhse`rggatd`m

Eihfk

Masibh

Eihfk

Masibh

]ruhnfti`h

è II t`gfca EI

Eùriar

trfhse`rg

gatd`m

Eihfk

Masibh

at







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







Rdy EI0



ih tda pfss lfhm


st`p lfhm tdfh II


gag`ry


rasp`hsa





gag`ry


at









6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








6

1

=

gt

ltImafk ei ktar

]rfhsear Euhnti`h

Iheihita Igpuksa



(H`h-Nfusfk)


(Nfusfk)

Masibham ei ktar

]rfhsear Euhnti`h

Nurraht tiga h7

at





è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




è eiktars

j 6( )

e`r D(z) 7 D(a )( )

pfsslfhm

st`plfhm

ω ≦


lt

Ϗ

Ϗ

ω

Ϗ ∜∣


Ϗ

∣



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



S W

jω jωh

j -j

jω

n

n

6d(h) 7 D(a )a m

lt




Ω

(h 7ύ)Ϗd(h) 7

sihΩ (h - ύ)(

(h -ύ)Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣

-G (h -ύ) G)


m m( )

pdfsa makfy

brùp makfym m

ύ

ωύ

ύ

ω ω

ωύ

ύ

ω ω

≭ ≭

Υ7 7 7

Υ7 7 7

Axfgpka 1



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Axfgpka 1



trfhse`rg gatd`m

sfgpka







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Axfgpka 5



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



p



trfhse`rg gatd`m


Axfgpka 2



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



p













b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]










b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



b











Rihm`w Gatd`m









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









at




p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



p p





Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Axfgpka 4







Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Axfgpka 46




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




jωa 7 a (- = =)

e`r D(z) 7 D(a ) ( = )

ω

Ϗ ω Ϗ

Ϗ ω Ϗ

Υ ≭ ≭ ≦

≭ ≭


6 ( h =)(h) 7

`tdarwisaω

≭ ≭

( )

=


=


6 6d(h) 7 D(a )a m a a m

lt lt

= 6 7 (h 7 lt)Ϗ =

d(h) 7 (h - lt)sih

=( lt)

(h - lt)Ϗ

Fetar nfk

h

Ϗ Ϗ

Ϗ Ϗ

ω ω

Ϗ Ϗ

Ϗ

Ϗ

∜ ∜

7

∽ ≯

∣ ∣

w

= jω -jωh

w

h7

jω -jltω



D(a ) 7 d(h) a

fetar avfkufti`h


=

ω

ω ω

Ϗ Ϗ

+ +

∖

Axfgpka 9



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



















wihm`w







tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



tflukftam lak`w

Fs f ]dugl ruka

Axfgpka 6



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



p








p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



p b b b p

Cfisar Rihm`w












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



e`rg






marivam ly Cfisar



Axfgpka 66




















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



















maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






maeiham fs














Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Axfgpka 6lt






















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]


















masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]











masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





masibh









asp`hsaIME]

at








nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







nàeeiniahts



Axfgpka 66









Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Axfgpka 6lt






eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





eraquahny è 4 Dz






usam









afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







afsiky varieiam






EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



EIK]A AFKIZF]IH







Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






Y(z) 7 D(z)T(z)













Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




Rdara

]dah wa bat











wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








wdind is maeiham ly



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



E`r Axfgpka
















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]















santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




santi`hs t` yiakm

Nfsnfma E`rg







_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



_frfkkak E`rg








GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



GQK]I-F]A


GQK]I-F]A M^_








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








ihnrafsa











-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]





-j ja 7 a iωύ Υ

id(h -ύ )

jω jωh

j -j

jω

6d(h) 7 D(a )a mlt


(st`plfhm)


Ϗ

Ϗ

ωύ

ω

Ϗ ∜

Υ ≦

∣























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]























M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




















M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]


















M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]















M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]










M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]








M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]






M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]




M

M M

M

I

I I

I

≦

≦

≦

≦Z-6

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

y(h)

Z-6

Z-6

Z-6

Z-M

Z-6M

Z-K

Z-6K



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



I M7I

I

M

≦

≦

≦

≦

x(h) y(h)

x(h)

x(h)

x(h)

x(h)

x(h)

y(h)

y(h)

y(h)

y(h)

y(h)

M

x(h)

y(h)I7M


`tdarwisa

MlMf

M7 Mf Ml

y(h)IlIfI7 If Il

x(h)













h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]












h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]







h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



h7

-G -ltG -gtG

-6 -G -ltG -gtG

-lt -G





∘ ∘

∖ ∖ ∖ ∖

-ltG -gtG

-(G-6) -G -ltG

G-6 G-6-(gG+C) -c -gG

c7 g7 c7 g7

G -6 G -lt G

` 6 lt





7A (z )+ z A (z )+ z A (z )+

-(G-6) G

(G-6)

G

i

G

`

G

6

-6 -(G-6)

G

(G-6)

+ z A (z )



A (z )

A (z )

D(z) 7 6z z

A (z )




Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]



Mirant e`rg

_`kypdfsa e`rg









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

MAÎBH

Fttahufti`h rfta






A]









]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

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Fttahufti`h rfta






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]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

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Fttahufti`h rfta






A]



]DI^ AHM^ ]DA ^]QMY

H MIBI]FK EIK]A

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Fttahufti`h rfta






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Digital Filter Design-DSP