Sayısal İşaret İşleme - Gebze Teknik Üniversitesi Yrd. Doç. Dr. Köksal HOCAOĞLU Ders Notu

8/9/2019 Saysal aret leme - Gebze Teknik niversitesi Yrd. Do. Dr. Kksal HOCAOLU Ders Notu

1/83

LHLET_IME ABLMDWHOHA

Z^L + JMKH

LHA 7:4

WKP@WKH K_LT HLALMM TLALHHL_

Prd. Di. Dr. Eeskh BIGKIH\

?6;7-?6;4 C^ DMLA

letrimit

Bkekm ^DLA _

www.lladlrsmithkr`.gia


2/83

j"HA

`lurk

`r*k`,,

D..

.h(``e

sk

+'rl

4 i,

Eimuhk.r

,

bcr,|*

9k]kkz.h

irlthlr

.

K;l

,H

9.-l,k

55*lmhc

.

Ky.,H

iur`

D."

N,"

.

9

-

Dr,

@,,,*n

Kmkh*

.

JrlHkm

\*i3,

KmkhT

`

.

rkl|-h

l

l

k

HE

W,}hlhlr

.

TH&

"

t)

'/,

h

"

,/,

?6

-

7i

NH

Krk

N,/ttv

,/,7u].

+

h;i NH

5

**|

Nmkv

Hk


3/83

h

;6

?h

?

hH

o`Ngrl

tl

-|m,l

W,]iU

9riglW

shk:

`i.rH

,

K7z,,*..kt{*r.

qtggk

*j,"Ytj;

sl

`kr8$rl

d2]N,7,,

.,4,,rl,{

4

C`r.+>`h5

"]kq,r

d,|t, C,


4/83

Oks`g

m

n{

I

'+

1(

{

i

,.4i

tHv.

7:+

4

?,cKJrK#

>r"'

,,"-)

_li(

W`mr,

ihNi;

tl;",l"gl

/jm}

1-

K

g]j

@

`*" X

lh

`[ ;

l)

lx

m

`wim `

UmQ1

hKh

hi(

lN

lu

2hi;-{z0

.1-)

Tl

]l

h 9l

r>

h

N,

,

hg1

7 ."X

i(1

j`>

h*h

hK

h(m)

"

k

y(m)1 K

rr

(w"m,+

?;m*

x(t}

t

x({+r)

x(m}1

Rtm,rM}

x

(")1

1

jYxkYchc

;

R, hm),

,

4

35

Nk

`(,],

+3m)i

K.l

'

@h-

`tum

-`?T@j`

Kl'

,l-

],l

n

*/4,

R

(m

h1

h,

g.i

(

*N

m

)

ln

i,

t

.;-m

,

-r-

V)

1

K,g-i(,"im*

)

VlhhG@N5e

,'/gl,rl{-

9*,">NlN*>

T

'l`,

,N

5

jvuj,}

tl

k4l,tlr

Kg.(Si]+')

Krlr(wk(m+,uh*o)

., i

K,gij

(-i44

t"hi

N.h+

[|

?3.H.

gkj(hh]|+)

,|>

:.;

s

@

Ht

?m

e

c

HmH,

,

2H

3(

m

xh(m)

1

gir(

Qt]

|

W)

:5

;:,

(7(mX>

gi(m)

KN7

5|U k)

Vgr`7*i|hh

-

Z1

Yh

n(5,

N.g

2

77

9

M}5

^

rhH

Nzt

T

,r.-

'h

}

4rj

',

]N

*"]

")

hz

t

`-4t

7r

r

xi(k}+Rh])

(i,*r,*,

i

-

....

.,

|

"t 5

0

;7

xi

(m),

{


6/83

|iH 3kh;

ilrk,*`*k|i;

&;"

lkG

G,

u,

(m)

1

x(]

),

7

t

m)

gt*1

U,,H,

44, N(,

-0,

5](',r

``")

(k)

rnUk),

Nrm

(i,"@m];

,]tt)

J]*r

lkN

9*lr

Whhm.*{,

|c''

`t

`h,.e,*,k,h

NN

}--.'*j,,,

jYr"

H

|R(]Qh

--} im)uk*

tr

ih

NK/NK.

rr1-

jx, H

(*)'

,

r"j

:

r

h

;1

j >YX"

1

dXvlr

;lk

*'

Lx1

H

X{k)

m>h

;iml-r.

hHH

@

H

txtmQh

|H+X

mr

-

e

7(m},

t])

-T{h(m}"

t

;7ti)

{m

5;8

l]l

/j

3

Y-)

,,i)

Kvl.i)*

Vi

)h*

eYh

N

mN1

;

{hirlYSr

H

h

.--**

R(]X

1

Gij

*Nii

u,Ni>

I, jr

X

u)g

s

i,2

3

t

m,1 H,-k

)

])k

,

;,?-

]

K*


7/83

Dhsgrl

tl

-

,Ur]kl-

>5-

xthN

h;hz

zi

h.

RH

m)

H

n.ml

t*

#}ltl"rm

h Kh,

z

-'`'Y

.TJYYl;

(m)>

x(m-,.,k)

Y@YT

h

,

i

9.

*=m

H

7

0

/4

?.

)

]4gh]j

Kvlrlj

i

,(]X5

H

x

("-H)

XN

7 H1-9

t)

`

hl

ih Dlh*,

hsh>l,"

H7

x(m)

|,ml

i,

y

`

l,-,

,


8/83

x.}

*--

u(m)

x(m-i)

--

y

("-]*)

i

h*.r

j,q

WX5hlr

5.

.

***N,*

(

]lN

lm,N,j,

h

it",]

yi]

}

-)

olhlgl

H,4l

hk

T

`rj

rr

hl,

r

m

(

HmrJ

,mli(l]l(

)

ytk5

(krirh,

ihh

m

'r`,`Nrg

(

*

Nlkrl`hhhY)

-

x

(m)

x(D)

G,-

rk

hh

}5

c(m)

>

x

Hm+h'h

NUi)

1

((h)

-

mi4

-

Gi,,

)k

(

k]{`

-

Gkuji|

Xr(]

)X

W

Ex

c(m'h

8

;*x)H


9/83

hrhiH/ihv

Bi"l.,]i

"H

7

ik

,,,,,.

Nr,u-


10/83

t;;

7

9

.3

h-H

h9

DhH

n

H;

-HhN11-,

H

-;

k

N,h

3yhiX

;

.tm'|)

;H

X;`

-}

,

{k-u)

btk)

y

-i8=

ct.- Y)

H

x,{m.--)

h,

Nrmt3/tr-

"'

/-*

m,

G

6.i1

k

[kg

I

o*.xt],]}

y}

(m-

;--,

,r

>,

-,ht

-


13/83

H

j

izhi;

(m)

- .

;k

NN

Y7

)

,))

{m

r)

-

{(

x(]-)

+P(

,k(mN

1

N

.

'N

0

tm+

h)

>

N

(

xtm,)

+

(

xrm*h)

+

xtm)

t

x(]"t

|),

->>>)

;

-

(mQ,+

0t].th)1

n,

@rt"+)

+

;;(kh

h)

+

R

, vmtH)-r(k-h}

q

(k4X''

]

4Yl,

NN

7

hh,

4

7h]}>0(]-|)

t

x(r)

y

(m+

)

y

h

]-7}

*-,

;7k

.Y,

nQ

H

*yU]-|)

+

x(k)

*

y

(m-

h)

.

i.i;h

|""

-)

k

r,

@

|u--

HN

n

*-`.`"(h

n{mth

)

z

7tm)

,

-N

h-h)

N

@

,


14/83

@xi]phl

',

N

(/)

*-

6,4

7

`,,-|

)

.2x(]}

,

k,qHx

, rrr{GY"m

,--,kutj

8,4/g,

Hh

7tm)-7{m-)

r x(m)

vi

-)

-.r,

N

kH"l-|Nk}`v',

.XghX

-

r(--,r

)'v(

P(m)>

9

*)

N`,`

},g,,]->,

`;5

h

j

,

";:,>,q

r,

k.(Gt

h

-.q'h

|

8N( -

N

,(

j

q

tt

q

. - )

)t

(k,

,


15/83

/

P

-;-;

)x

,h

K

hYY-Y+

ht

h

+hh

"N}

y{Yk)>

-

n

,,

h*

1

lY>N*

m,

+

(*

)

DrJT

D`Nll"(l

Gi].,phlx

lpimlmHi;

r

mj

,-

{-,

@ut*5

@

K hY

l-

h,j5

^

l

YY---,

R)

|-}(

.r,)

1

^

,

()

h--

i

{t,v)1.

H

R(H) l

H1-4

k(N

,

q(|g)

P(-)1

;

N

h.*4

HT;

`h-{t-

-

n"rh.-

-}*

|

l

t

H

4 Kh

gt

kZ

;

>,,l]

Hn`-)

YNr] r

b(h.)l

G/-

h>

-()

'***---*-**-,-r'

x/m)

(,r)

Nkrl}r

N"j,

,g

l

&-

t,t,,,k-g

_gr3im

3"l

,

.(r

]k

{kt,r@(-r-

N,tk]

'{u,,"-

K

x

1

z)x

L,

e9m'"

lm

wl

g,U*r

)1

|,(-)

r{.m

{u,]g

|,ki

.k

Z

,r,(,

-

i`-m

-Nk

,N""N

`

(.r

N(.

A.-'

)r'

rhgH

tg,?Hk

kH4-";,

,:*t

i

oh

{5

/

Y

g,

,"

h

"*

* N* 'H(

}Nr

q

h8

5

4'

"

'

'],

,

),,H*>

m

lNr

K.

h>]r{3

.

vl.lglj

,],

t

@

@

`

-j

4,-l

`,|

4

)

nvN0,.X

l

j,.h

I

,`

ru,

m

`

'

------,N

B

(-)

h

}(*/

*"}

H

-

h+,

Uv,,

)


16/83

;H]h

Ht

hiH

h

?.kX

R(])

-rU

r

h

Kxk-,ph

l

>

tB

t",)

h,

`l

l

K.g,j|im+L)

,3HkX>

K

;u\]>)h

*j

(u,,"m

*

*

)

'

n

H,]+k)

y

(m)

1

K

l-

;;-r.,

+

&)

0(m)1

h

hB(-)h,l

4

-

@*H

B(,.].`,

-

bte)

l

H""q

m-h

k4

-;"-'h

}

(-NrX1

N",t*u

*4

M

Y,(-+'r}H

X

-

'

b {\h

l

{ u.,N

?T(

- HY

ThX--

H1-4

,Z

-nH

r>

, X i-'

l

--H

'

bteN

l

Z>

,

Ih

+.|,

(",

)

>t-

?.r

N

1-

(

$,g|*.j

l4

r>hsgH

/,

r

H

"

{

h,]-^}

-

)5

.Q

-

ym-

)

N

},{(*.),

,r

.N

N

,`*Z

l'>

+ N.

,-l

-5N-*

,`4-

N

-h-

/ l"

lX.

u-N

+

-

(

u'

4--Y

".\

",)

Y

.]-h ;

l

'

s`k

`,]

-

-N

@

k

h

1N

9

-

-`

Hm

4

*9

W`{

N,

,'.

k

>+

Ktg

i

t.

q

`rtr4

j

` tN,j

q

Vlt>3rN5H.

i{*ir,

{*h,].i

dlit

H",,3]N

>he

`Nli(

bt,i".sW

$

h+l,

*}rt

-

;@

;t-}h

-'h

k

-

:,


18/83

iXhk7h?,,t,

LY

7:,

#

4,ukrrk#

`5H.

T

`

:

+k

5`,

;kvH,t

k`

Kv;=KH

"`*"

-

(*.)

.,

m

--L}-*

"4

`,],m

-rm

rY

R(m)>

l

+

g

, .

n'']h.,

@v,)

+

N(k

h

>

;l>.5"4(

n*rm|N(,r}

.-0h,

,-7`m,h*hck`yir

-rh

q

.'

+h(w)

`"k

th

-)

j

'

x{m),

l

3/]

T-|

3H

kX

-Y

-*-}H

n'>Yr*

hwk

yt.,>

lN*(m)r--

N(m),

Q

-14>>Yh--'

K:

y(k

)1

'

](

",-H)

x

(H

)

1

L.>-d

6i


19/83

i4|i7jz,h+

kUm)s

N

tHkX

1

u(]h

/(,r}

*YN--

@rt.}ty(m-

(.,)

+

U{m-h)

1)

Ptk)1

9

)

*

x

|m--?

*'h

("-,)N

.T

t

)Q

)t]N

.k`mX1

Q

NUm)+ }


20/83

iXhiNh

z"9

jtlp,,l

8m,|kt,ik

'

,N,U

y,(])

-Y---

U

tw )

y(m) X

P(w)

Rt*r)

(

'i

,{

-{h

t

l]

t

U

""

(

d

]r..i(N

)

,)

h

U,,{kh)-

(

64

m-64

xkm,p|

?-

Wl-3u

lm

gl

j

iu

r`

lr

ii

*N-]

((w)1

Hx(])

H>

*4

R(-) 4

id

gi"

N5

t`

ii

k

o ,

hu*l

uuk

h

]]

*{

hkH

tip

h

l

]

,5h

r,

hrWY

},ivrX[r

$r*

V"]*

v,ir,

;

r

kikru

*usm

N

"

{(/'X)1

h

{-r

*h@

t

t

XHt|Y`

;

b(r,}

1

$(*}

z

]

itr,)

>,rN]

-N

hU.m}

*

-

n-).

(i,l

"-'

H

]

H

im

(m)

l

-

i

H

-k:

M

H

i

H

>

-N])

H-l

hi.-n*j,

hkt

(

H

:hr.rN

g

N'um

rlr

Zkrd

',

,|

r

*,{"*",,

|hh(w)h

Y

7

-


21/83

9rk9l.+,ls

k(

Jihr|lr'

;r*r{",-

R,(m)

- -

R;(,)

Rht]5

.j

,

R;(*)

k

P(k)

+

o x?tm) -, k,

RmU-)

-jN

x(])

>-",

R{-)

,,]-]r.H

l'N-m>

R(,,)

x

t..)

N-"

P

t']')

mtmX

*L-

"t,h

Y.

x(""'},B(*)

x(k)W b(k) 4-

X

tP.

N

x(,])Ft(,-}

R(m},

t]tm)

Y+

zr(

-+

o

};(-)

kX|

ij

zk

-

r-h

l

jxkY-j

hc,

--;-

Hxi]p|

,

U(")

xth

U

|t")l

H

+d]

l

N

x(k'h

1

R("r}1

R(m)

,

Z

(".X

1

(z

-m")

-

`-m

t]-",;

l

l,h-m"

>>,r','-.>

P(-)

)

{*)

x

t,p}

7(m)

1

yhmh,

1

9.

-N-H

7tm-h}

,

1

R

{-)

--`*,

]-H'

;

H

..](])

-

-H

|

Yn*

Y

h t- *

l

'

@

H.N

X

,n-;

j

*N

l

,h

H-

t

N

Y

Jh(,')5

q

k-,N.

z

-TbN

l

h)

*)'

](m)

1

(

,

?k,

-

u,3*


22/83

iuj

"

|

zi

h;

JT

dU])

,

R(]')

*.r)

j,U)

*

|7,,

`5

N5

,=*r>ir

@

m

gl

@lhc

o

`h5rr

k,

-j-

)

ym)

l

1

HY"

]-Yii

Y.----.

94

Y]

h

h-

h-,

..

y(m)

3

h+>"rl h

H

]1-

d`]`h*G

;kHi

}

?

N7

]W]'

,] ,.,,*.

N5]5)

.`u

v-k(

r-YH

`q5k

{iur

hglm

v5";ir

,

N ]h1-5 7ij**Y

5}"l]`

'`

;qh

(t

tkt)h

-

4

nrx5j+r

t-h

r`t

H

J

,;

}il,8H

h

hru

N,

r-,

N

v

k,;-

r

:-k

;

,)

+-

k

hh

8

iG

@lh8 hih

xkr.K9

hl

,.

R

(}

)

1

*

"(])

+-

(-

n)]

Yh

H,

`,

hkh)

n{

=N

N

X]

;)

m)

>

z"

hh

h-->-

XN

-

``)"

H

-*Y*. +

-t

h-H

+

3

6

|9h);

q

)"

,'

)

h+h

ut])

P(}1

t

*

++

N

N

h+h

8

z,

(r>`)

(i*nQ

("-t)

-Hn-

-.K


25/83

,H

/

q7

/

zrh

Hh

j,xi]"0hl5

##

yk-.

hl

`

y(m)

1

(tP

*'")

,"(-]-|)

&

-(n)]

=+

t-h

'

Ei">*

h+|

(

n

"U*iN,n,]N

im

Nomh

N

5*.5

,3k hh

ur

4

k{m W

hh-|

i,;

lYrw`j

. --4Y

4

+k9

k"

,H

Nq

";

-`*(

mt(

I

ih.

`'l

..,

]-k;'*

g,

Nt-

lv7q,bl,l

lx,,lV+

R(

k

)

>

)k

h

Xi

M,h

j

/-

m>I

-h

X

]N

)

R(+),Y

Yx(khk

R(k),

-

(i

9

H-:k;

"

,.}

'-j

)

r,

G

|9|)

R{")

1

x(T)-*

314

*h

Y

44

/k

)."

(rI

.*+c

1)

,

9

4

-

?+*


26/83

9r plr{,lW

i{

,)

Yi

gg.r,m.it

8ik4''k`k

imh

?)

|+

x

{m)

5j

r``NlN

,

7)

hU

r(m)

lj{


27/83

|67

h

zi

t;

`}5,5]

4k-ol,-

h{

-Ub5r


28/83

hh

G@7h

ziht

Y T `.N.k

-`.r,

,.

-;

Lq,i9hl,..

xtm)

1

.m

.ij

|.-i-m)

'("h

`

'm

H"'

,-'

'

N

"']'

-5x(z)19

Y

tY

U,uYn-,)]*(..->-")"N

H

H' 5*-,

X**Y]#

4i,

9*k

3-,

,

+

?

,.*(]){*.,

z

u*,|

@

-)*

*

@

-n-")

].](]h

.-'- ----->+-,

(r.

'

,

Y

(.l'

k-rH

r

h

--*-r-,

{m)

l

h

|

,-,'

Ht

Y|

H

h h-r,HiuN?,|

'

-,

h

H-..l'

h

Y?rgj

uNg

9-'*.r4-H

@

+N

,.

h&h1

r

+

{)

m-

t])

+-,

-r(m)

jhy

>

h9

hk

=

)

--+

h`

`il

,,

N+

)

x(])hm}

H y,(9),R

x{,,)

5Q

R

h+)

hmvl

Nl

N

,

k,]m`"j

kl

k,

.H)

h]


29/83

hh67hku0

;

-h

-hk

-H

z

1)

x(z)1

{})","rr,")

h+ ),

p

k.3 i.",],

d(m}1,Cru{m`+

?

{}-"{]}

Zl/>,3


31/83

Ki1(m|}

K(k)

j

1

9-

|

?

K*(l-t

m()

h

,

tr@

hX

1

RtzN1

*

+ t(+'

-9z''

t-'+

9

}-kY

h

t-Q

h@67

j

u|+

N

+

Nl.l"l

( t*,,*.N*.

,

H)

d

*

33,",h

,,(

@

H

N*

Hh

H,

(-

*X

n

H

,-'N

(r-

,

*-

)

H

H

n

(9.h

;

7k3k,"t

L,hlglH

R(9)1

*,.

KH-

+

(,

-

t

l,,)

KN1

(r.-n,-')

x(t)

{1

',t

-hkH|

Kt,

Ku,

K

N

'|

@

@

4

H

Y?

-|

+

|:`,*'-9

+ ....-4*F*"{4r

#

Yh

YH-n-t

-

7

-,)

(

-H,("i- ,

/

h

',

`

u'.)

-

(-

`)

(

;;-+

H5'-5X

-h

?

h

hHt

H

,

-

-

-;-

-;|

+h:9

-

+;

N,*

-

-H

`

7

-HH

,|

(+)'*(.)

(

+)-

;

'

y(mX,-

-

Ni-

)"

-.

h]) -

;g,3

u(m)


32/83

h

hI7

hzkc

`m

r4TH4r7,.

mQv

H

-,'

:

,;

N

Nlm,U"-+

* 5Q

rl

5d.l

(",]]

,

N"m)

Hr,J,

h.

h

1

Y,"XQ

k,

hn

N

..1

j

,,r;

p-

U

i.j

H,

j

Q

-zh

i,j

i+:9-hm",

+ou,mt

RHt)1

Y`.,

-h

[kt(}'+

.,,

,

[v,9

A)ru

1;

,

'

+Y{

k-'**

*-'* ,-'

R(k)

> >>**.*

h

*

h]+L}+"

j,xirmp`,c,.

-,#

k

j'

HH

^

R(tX,

)

Q

}

@rN

}

l--

-z

+

;;k)1

ut])

*----r

l

i,

u

tk)

9,

3

m.u

(m

)

*-*

x U]-M}

-h

4

'>

*

Y X"-

(t-9

)

\*-/

h,

+)

Yj.N

9

.`

***h*Yt

(h-,

,

.**.-"*-----

-

th

)

XtX)

X

H*."Q

t)t

t+

h

)h

'--r'"*-

",

""

*Y*i*-"**-****+**-**h",-'"--

-

-h 6,7 h N

i,7(;;g;

Ru4",,,hr,,.

o``hhl,j/,,

]Y

.,

*,/

h{6.7 ,'

N

,

uj

g

(

(

{, "

X,

,'-

X

X' X

i'7,

z

,.,..@

k

k

-'"'

;0

''

"

,m''

@r..

,

m'

@

`

h[

r,

","

m

N/

.","

*=


36/83

Rr

(m)

5

Rh (m) 5

g.rj

i,P3t]

G.kj

h,H,"`{

4

R

(m)

>

(g{

u-s

rX

m;-

-

6,2r@

vc

},,H3`

,)

R,

(NH)

"

R,

(,-)

h5 J.r{lr

1

x.

(

kr

}

`(

k

)

.

x.

(]r)

((+)

P


37/83

O@i7/zih;

---.

h

Y

@

N]-Vh'])

h

x(.,)

*.-Y*.-YN

@

x

UNH)

K7

-nmYt

x.(NH)

1

gTjj

h

8.t+}N

-

|

.g+)

l

Nt

-r

li

Y`s

xN(m)1TJT

@xrt+N

1

N""tt)l-

N{

Yki

k(

-`wk

R

Rr{

Nu)

R.

(

--jHr}

+

Rgh

*l'}

*

Rg

(

,/H

+

N4'h

t

-]

-H

{

."

;-X

(r

(

5)

t

K

..ltNg

.

Y;

X

*--

,,",/

Kt(

,

``g

*m

*

tH

nhh

"hd-j

,,Nq

-*r.]''5

Ng,l"

`

h"'r,

3/

Y


38/83


39/83

-hr;

/

TX k.(Q,kghk

hklykh,

k

K:

-hkj

,

,rhjh

YHjh

,hhk

-Lm

i

rT

`hTr

?>m

-.

uim

-N9m'

--

r*-@YN

'&."h--

-

)ii

-,,m

-:'.

i

:

,

t

*2m

,}m

m

$5>55

"

tm

.j

,`g

-X

X jt

(

:^,

)

,)

-`8--Y-.

-

h,

'N

).,,,

N

h,,--4(>.

K

;`

N

)"}

Yk]5N{`j

'

.N

`hX hX

m

/X,

/X

/

XYh

X*/>X,-h-X/Y

X

'

,,

*9$

Y;

;,

3

r-

H4

3{-

R(t)

qHtht

"N*k

j,Hk

`tt

&kt.` k'j

'k

].K;h]h

hkJ?i,

r

,`9

-l0`

'o,,|l

?>r],

{

h;,

l,

;;i..l

{,-]

o

i]{

h'{}hN`?*;

$>h@,

g

Y5"'H-

,, Yt

l"

,/."

t

h"k

q

`'j{

,5j

,*(,

.*-

-,s.,,-...,-..Y-....*..,-,.'**,:}

-W;-

Y

jj

7

"?r

.h

ir`-

gr

(

zz-t

)

..**

`,g "H.

,.

{

l

*

t

,.,5,> ,,n

e

i

t

N8.

gN,>t"r

h,

rtht

"N*k

*

7]


40/83

?{/67

h?i

-hu

`k,`

Y. `,

'

/,

(

y*,#->

}

ju`{N

hjh -jr

"`,

?r|

1

3;

,

-

70-


41/83

K{j

,

u*

;4

` 5

..r'|

(>(?jX'`

-h

,,---

"'.'';

hntHN

YY}

d4

H

i j

.--.-

/,*k

X

'Y-/

Y`QY1H-r->h

Y.Y,Y+

(

bkm

i5,m

+bl

W

i,p`@k3

ei{l

.

(-`

}

Dium

Wim5,m;

v,

N`Nl.

]j5m9

T4?-T

T-+

Kk

T

xr(

mk

)

7:hp7;?Yig

*,Y

}:

H

g

,{*

hm

`

`

`.]-

Y-}

gX5

tY

5,t*,

--;

}

;t.

,

N

,``

*h

{'

5;

hd

*

-.0

h)qbk

Hji

rN't,

?

],h

;,],@

Z>h

[.>?

/]XY/4-k

..--*L-*,

/

--"

h

**,

**,-**---*---

rY**'*h

R7(m),

R

tm

,PT)

-

t

g

`*`

c|iw]Nk*phld

t

T

x(r)

Y

T

q

@

"(

-

,"+y}

DTjT

9

x(")j

rrT

|

(mN

tYYi

i

xr(,)1

h

H

x.(#r-

/4

T

e-"*i(

`tZt4

]

r-h

" h

'

,

",

I

hhX

pk

.)

hN

t1

Z.r,

L*k

1)

u--

`

*)

YYX

H>

H

,"

r

I,

.-

,;

rK

-

,,

t"-

h

ph+h

,

-.

3-k+

;.

H---,H

.--t*/*X

.X

*Yh"

.-

..-,----"-..- "

+

A

-?m

h

Z*-|

Z>i

*-;..",-

-]-.---*-t

N,

a-h

I]]

-qk"

xhr}

1

H

.


42/83

H: /

07

/

9Yg ht

(

`+lr",))

/

?rr

hYv

X

/'4T

/

?j`H X

h/

-

.?"y

AT

u.*

;".m

`

Y

tqT

-,

b`

Y.#

qT

/

X"N

?r rX

t55)

h]) }

R. @

-->

XA

-

-T

,

mr,

hm

H

,.(55

\1

-R'

jr

x, hy'n

Xr*

-,

N

(,

h

V-r

e7-r

r.r,|

-r

;-

]-rT

`-i

Q

X4-

YhrH

,]

3"

t4-

Y|;.@

n-

A 3]-T

-1v

R(

]h)

1

3

}

(",)

TYr,

(

'-

-n"-i

)

-T/

t(-).

K1 H

`q,;4

R7

(-X1

Rk

t*)

1

Y -

K

"

^";

-'*

(

-j"')

Y1

)

@

K{

`h

t-"})

/

n0X

*

z-/

,-i

t,

,(

*

(-(

'r(j-jh

`)

k-

i

-;(

-jrH

R

U*)

*+-


43/83

H


44/83

(j0

XN

;3 |

N/

T'

-

T

hH

1

R.("

T)

1/g-("t)

1 tl(]T'}

lN

,

? hinhzi,

|{(]}

*-**0

(,

j(

?.;;

X

-

c)

-r;

x

(mh

x

(]

j

h

kgjGk

R:

tm)

9

h

@

@

@

h

h

Rk(k)s

x(m/H)

u,V

J

ck`m

H-

gY+

k,h

Z/.

K>

k,

0h*,

i*

..

v

` `[,

xk

U-)

+-TY*'

x(4h

ky

R5(m)

-H+7-

HH,

;H,


45/83

3h7h^hht

N

Rl(

(H1

h

Y,

"

xl

t,])

-

Rl(m)

D,TJT

DTJT ;xl{](

@N

xt4)

*,{

i:

,n'm

@

*t,.)

H


46/83

?

b

("-e)

h5",h

v

h,

k

'{

T

Nr/

I

h

H}H|r

-

4lY


48/83

Iu"}. irr-hW.,, )

k)

xgt)

Hu

7&q

#

0,ukrrl


49/83

xt*)

*Hm)

-L}*/B-

'5m,.rh

h,'>*,.

i;

Nr

`l"`k

>

k ri"

3k

i,

h-,

I,

W/,|

)

,

B+

-h

,h

7

U-

U

-.

U

-t

]

{H]N,-

v]r]`k}

*

;]jm},

}

Q

4q

-


50/83

Clml.|

-|l,Zrk

r,

m

(m ,

`]t4}

,

k

K

h

i>

)Irh

og,7

",

t

8

|

k

i

h60

|ziy

`

{,

rt

h

h

l

r

Yr5.,.N">H

gi8

(t].-+

W)

i +n.

x(m}1

R;",,,K/)

x

(])

-

K,

'`4

^j`

i,]

;4rthkh5Hl

x

(m+N

)

?

r

-.

M

1

?,r

ZY

W,|H

H*h`*,],ih,n"k

rt

Hk(

>

].I

h-

5

K


51/83

x(])

q(4

)

--7

N

,

-h

--T

h-

h

*YN

H5]l]/,

-h,

],8.

h

mvlr`qm|-

(

Y`]8c.r

}-z,]ik,(k

or}k]r?r

m)

i

1 r,()b("-e) >)

HY1

*i

1

r'"-\)

b(H)

h-,

*ii

Hh

.

h

?ih/t

Kyr|"

}i,*lk-,{

,}"`e,

h,8h

h/imvkh

Gh;ik,

Hm)

1

R()

t,(,h

H'r

h

`t

Ul*

,

NljhH

lH

hhl,Nl

,z,"

hl{,h`5r

h'

(] X

.t,.

Y h].H KiYHh,* } h

l.--Nlm

K,jrr''g-

z)

N.5hr([

"r-">>,

"i'e

dk'el

*0

X

'5>',

,qj,io`rr,

}|ik

B(

h

N

)

m-`

h*,

v]r'

)

rkm(*3 -

n8-tl

Nt

.. r`.

_ig

t.5-

l]o8`

n

.n

{"+

)1

y{

+)

hkv

jl

9

:

N1

tl

.Nimt

|

-k',

]`

t}

.|k7

j

k.,-H.

Lyi

,*p{l

>

R@m)1

..(])

]

b(h

1

k,7

&7hl

K`,,

ru

9,`-

]

Hij;3


52/83

j

xi]ph

>

btkX

WhkX

+

x

(m}

7hj,,q

;

N(]

-h )

7

{m)>

y

(m)

+

{kX^g;

?

x

(]*`)

?

k*|"}klNk

nhu

k.3

N,,k

hdj

l-

mhN,

,

P.mX

T_

yH

{;-3hk,r

3"

H 7,kNrl

k


53/83

`]r,i,kJhl

.',

P(

9)

U

H

P{})r,

?

7(m-)

-)''*

h

h

)

x

{k)

1)

+

0H])

n

R(4'

Y

r(t) j

"

H

b{m)1W(m}

+.lrt]-|)

-,

h

Q

?4

N

ht];

"

h

-*--.H*-

'/;

\

i

j

,khh

h

,zk

0

*

t*"*.

7>

*

O*.*4

`k,>,q&`

r,h

`

H.m

`

jh

g

}l.

5`*38,

-

v,9

';

g

@l..|.,.@

m,

ht-k*

}i'

e,l]

4

7

x

tm*|}

kgl,

hg}

Ghh{hkr

H

gX

,

Vr

o

h*-

G.zN$

`}

(-]k,

|

P{N,

|

.,

;m-|h+

xhm`

h

P(i)

, "N"Xt-y{')+-

?

";

)

(m-|)

Nlkih""*.

*r.-,

`khyiX

vk.

7

r";.

y(4)

;;]-h)

O

i

}


54/83

i

(

/,?

H`

h

?H/

W(])

h

(m

)

*U}-

* (7r>,-

da

ol

_,i,

j`*,

N]

ivNr-*

x

t"YQ

>

k

U`.

`

.:t(m*|)

+

5q4>h.r

j

q

H*i-h,

iU**r

N>rhl,]

H

r-4-p

7

W,

,(

vkr

)l

]t

h..

b

(m

h

1

`N

(

k

)1

-,

{

.

(t)]

.

-.,

h- `

9

h.

YH;Y;",

(-n

@i*

t")

@

h,

n-'r-'r

'

Pg({)

555;Yr5

`"-[

h

}5;mkh

|

;t]-

Dhg

,*N

7rh

3.

t

3*}

+

,-.*}-.Y

YN-hN-*,

{

, `,]gt

h8*8

h-t'

.-h

?,`

,

j,"

"-,

,

-YNYY*H-

.(,

{,

+e

?3

'r

iH=5**--

*m

hrjuh

j

,

r.>

Hi}, rml.e

hl-*rl

{ml.

hz*3, h`.,,,

*-/;k,,,h,,,,

-


55/83

,r,r,

)

h

t(*.,/h

t

-----+h

`(`Y",

;

,..,,h

z

-


56/83

+

-)'

C.k.(>|g

73hk

gHg,

]

,u*

t*7u

*

kl*Hh

ihk4

/`N

hz,,;

,,r,`] ,k

ehgH

it-kr-,

`

N lih

lg,H,c

,

;

^

H*)

*

]N

sJ9

;2,

t

GkmYhi,,t}

(]i*

l

;

?b

Z1 H,7,--',

-`*-mJ

&

-aht

^

U-

}>,,

,*

-,j

@

hgq

h

i+;

-3*m

tV

,`d,,

|5]*l.--

tk

j;-;,,h*4Yi

n

Dlh


61/83

Yjr

h}rq

-)

b

(,)

)l`7m

r3H

|err

q

H,

hl8hs.

-N

lhh`

z"

?.

b

(m)

7.

rlihhtl,

-.

g,m,3-tl,.

h

r

*Xt+)

1

;

Hii,

h-"

i

j

-h,

H,H

ku

t

Z1h

9

cHm)-

t..

hz

h

juk-,|l>

t

h

h+j,.

')"rr;7

hj hit

h^iht;

+*

K`9

H`mlgr

j"t.

NkC`

hgirkrh

--->>>

*

H

8,

EYju-]9,

,-9-

|5

he-lY

7H

y

(m)1

0;

x("}

kkl

((mh

+,

--

x{,)

F

b(k)

.

-H

9''m

;;

+

",

-k

^;

-+,

-,

0tk)+?)t]-h)+",

+

.Y

H

Ilk

h|l]hlz-5

yrN]*gY

`hg

nrh8-.,`

k,,,kh``

l

N,lr`t

-)

-hH

;

c(]-tY)

1T

Z.,x(m-H)

Z1:

y(m)k

kt

)

;,,-h},xtk)

''Q'

,

>Q30H]'

g

y{m)

.#

"-,r?Hh

g

R(.)

`

(

) *

(

,(;

(4)

h$t-,)

h

4h

.

9-


62/83

9.H@ih\;

Ht"t

7:`

#

Hi,

BkJh

K #

sKP,;4H

`Kr,LT

`l,-,l*,`u

THH2_,U,

tk,.ikdk

rkgHtx`kgl

hlmthztl

rkgHHl;jkgl

K0r,U

4k,qk,

o'`t,,t.

,

,,Q

x

t-

U

$;w)s

l

,

H/Y

t{t*,)

M,,

k

th.,

gk

b

(])

q

(i)

g()

i,(?N

[th

H

u>I

u)

h

ex1o

x1K'N,o

K,-o

K,K

x

-Y

Kj

i

x-

(

*Khhm

jh

l

*

Ni

qvkr{,k

B()

;

$

()

|

utt)Q

HQH;.Q

JH

`v;

9-

DW

k-

N`k;

`k4i*

F

s+].+

u{+X

Hcu`,vli/-

{rlh*lk

rl'jk]`9

F

gk]'iH

mkHm)

1

@DT

tT

"'."'N

1)

I

b(k)1

b4tk),

w(k)

N)

*

r]

jj`

7..X

x

o)F

bHk}

[crqHl

*lz

Wkkrk

hkkvihg

l+-ltc

``,

h{7(.],)

1)

." `)]h

j`hg`k

HY

llv

Jr

hhr

='

.ih*-

t-

3zn".g.

zg

l

HrV

btk)

9ir.]i]

Niklr5

m

N8.

H.im

vkhl

l/.-.H*`r,

j,.lt

"-,.

r

N,",]l-.,`m

Nl

F

kr3

]kh

-:i,

1)

B

t-)

1

JNN

(-)

F

v

(,)


63/83

wHw)

B

t,)

F

w

(,])

+h

("")

t

iol

F

Hht

}tktl)

t7h

lhNl

l*,-,H

`4lrt,k

BF|

8"h,*,

w(-)

?HhiHth?ih,

,|

miu

W

irv

K

HmNkr

,N|

.

dl"(

plklrlk`k

x,

`4

i

,

Ni,;

Lij

@]Nrj

k

o,

im-h

uGm-|)

`h

.,

7

t]) -

i

3Hm,hX

1

.

-

Th(+)1

og

+

|

9

-h

H

-kt

0(i)>

I

yt,h)1I


64/83

M

0t])

-

H

]",

eh

D

k:gT

i?h4

3

N(m),

v(m)

r

v

t])

xm)

jm

cHk-hg)

1

'o..

xHk'H)

H1I


65/83

(`n

{(m)

oit

Yh

9

x(4-|

)

-h

H+H3'

-t,-

H,

j"tl.

M

c(k)

1

|mt',)

|1

i.

-h

;

x

k)

b

ti)

h(k-e) 1 :(m),tm)

9

b(}

Mhz

+-'

1

Tr

H1h

7tm)

+

b()

8r]-h)

-+

b(t)

x(]-;)

+,

-

Y

7)

Y])

9

h

.,5,|

+

]h;

-9 -

9t

991;

]'

{t()

c

U

u

|t-*I

9

(o.+H;ct-h+

h"" *-')

Y

H-


68/83

;-0

|

i

|zit;

Lv

7:+#

tH,@+KJjhK#

,KvN4H

`

K_T

`rmMh

TAtHHl

_,t,

[rr`;

jir,.hk.t

ht4)

;)

'(.

(*

B(tQ,

B

(-;

31[

k7(],h)

-n]

-q

N?-

;tm

)

o`rlH

.`{

(+)

g

,n,")

l8Hl..

glvqj

]

-

Hi

+

h

+

-h

k-kt

v()5

oi}tm)

+

tr

;;'-|)

(

].,]r-

v(m)-}

iPt]-|)

XNr,]u

,3,

k,

s],


69/83

-----,

U

-N

c

Hmh,

>

}

-3

-7

Hk+

.

-7

9''

-

9

;.],

h(

I,,`r

6,

----:.-h

tr

(.r)

h-.-

,t

ht,

)

(t

-"

T)

h-m

-j`]

{H+)'

"i

`,

k+

h

X

*r

-)

hi

N)

,0m*+NX


70/83

)trH*)

1

'`/X(i,

hrr+4

+(kt(i,

;h

-+)

`)

H;

hig

hzihP

{(*)>;

T

-7

Xrr

-@

H

/(-)

Zl

h,)

-^h

X

h";

,-

Hh

`H

;

,u

N

;-

|"t

l'

q

0

yg(n )*Pl(5-

T)-

X"(t-,h+Pl(`-``

jr@

H+

R

(w)

;.t-)

?r

Y9m`

h-

m ;-

-

:0-


71/83

:,

Hr|]-)

-

?

N(],H),

(-7)

+

k

t(..-Hh,

4

hm

-';)

-

z

(m-j)

?,c hi..

?jr8t

H,

m-Ht

-

Wtk-9)

tk|

1

tm)

+

0(k)>

4

Hm-h)

x(mX>)

Uh(*)>

{

+

P(h"

q

}

-7

-j

+

k +'|

-

H+-H-,+

-,*Nk-H-99'7-

*+

$,@

H

q

k

Wul9

c5

h ik--rk

Nh-l

HY

Uk

;,-,

H`hhgkk47`+"

7nrm.,,8"H

` g,rk

kkp

1G

12

NE-

V()

c(l)

1

[(+3

i]r*i4`i]

D

`rl

gt

(-i]9

u+i

{`l,

H.

H,

7.

4

(+

h

"/

---.-.-,

|

*l*hpi"kjy']

h

"/

.---'

Xh`klkr

i9V,

4l5,qX`

k

D7`t-(

{>htlr


72/83


73/83

y(t)

H

?7hq

hHiq

9-hkk,

Q7-#Q

0H4'h

3(])Y

H;Hk*h}*

=`h

')

-rH

-h

Y-;

NYHl

+{

-d

jH

h-

B-ts)

>

i

-6:

I

--

NH,-i

kY--

+

N-

W1 d* l'

N

u.

trh

@


74/83

tmkt{k:"

))

.j

Ni

ti"

h

.lH.]Hl.

j`h4Hr

i`;k

j

k]ityrr

Tiih

q[rth)i'

'l){t

4

'

Gk|

,|rc

ghr *}

Dtrl

g

@

`

J(XYk

-)

lr

t

{Yj

5),rl,hr

o-|Hk,]ti5;rrt9,)

))

srti,

(


75/83

THH

j_r

Dlr`m7

,1

.H

(#-,X

H1

h+

sTh

;-s

T

@H

>

nsh

ik,kH

H+ `NHT

hH

@Y`n-.hhH

> NhY

lN

---+n

-.

o

Ohh`

hlkr

'T

rl',`

;ir

]k

4

9

g,

B](N) --

t4

(k)

Ng,r8kh8,',?"'k

K,hkn

srl,h

Nn{+-h

(+,l3l


76/83

tr*r;

$-k,*`im

i(hi


77/83

,,,T,"

(

i:hiqhzihq

4

-/

N:

NH1

X,2^2

H

H.H

WHg1

[.

hi,0

|\.h`5|?

"

dri

hmY)

;,0q^h

-,

m

.t*

X&Nh

H+

-i

iN

(rt(l,4|tth)']

)=','

(

z,u

u,)"m

)

7i,:z

?].

@i7?,qH

=/

hi7

7g,:;H

ci(h

ihk

gk,`

"

N"m

m1H

ih

k

8

(

l]

-z)

h"iGk

ZlrG

G8,t-

Y

D5`5tk(

j`h+,l,

'hq

:i`;

,

Hkck-hh4-

Z

i,;``

`'

0r,

M>

?r

hg

1)

M

1

t'

(

1

,1

0

i

H?m

`,'4

0t

Mg

Hrh,

iX

M,-

">

]'>}

>

],'

T'

h5*

.(uk

.kw

;

r

ijhKd

'

,

iZk|Y

k

tr[

,

|

-N

Zl

N

]`k

rl/`7ithkr

4hn+

h-


81/83

i)


82/83

7hihHi0

LHA

7{|

#

WKy`Kt

`ll

7,

BKJ3K

#

`{r

k

h

rc

u`

t

l`

DTJT

:6 YN-m

R

(.'t

,

@

xt";,

l-

r;1,

]X@1

?T

M

Dj

-r

x

(u),

Kw1

;c-;

j

xt"

m1I

i

i

b

m'

?r

j

/t

,tr

hh

N

;-;

JN

?r

Js

-

U3kq|-hl*k

phlh;s.]r,

J.

4

-rH

zc

M

KJW

Hr

tg

,-h

-

tr

u;

,

H

`(")

,l

K>I

H]5klir

G,m

viU"B']

,(.

)(i)1

j

r

tt)

b(m-

e)

H-*,r

G`rg,Hk

)tmX,

@Jk

(

xt,),

r'

hDJr(

R(|)

hN-N

(.

7FX

1 H-

hh.

I

tu

"(]-HN

IX.YHT9

-

KDD

iZLlH_V

-

WkvJ

-|

N(m)1

;,|t),b(m-|g,

i

0

--

hJT

(

R

;-;)

1

((+

(

x,

m

+r,X)

)1hh

(b,

*r-|}

),

tik

hlx

*"'P

h`g]j>ik

M'

/|

Q

thd

km;

hlr

]]-th,9j5t4,k;

k

Gkkhihq4`ik

tN-h

M

H

`tu;

g"-h,)

h.

I

B(w

+(H))

)

((m)>

K

brm)>

2

HNHk|

.

K+O

,H

-H-


83/83

]N-

|

xHH)1

x(m)

m1I

mNk

g

mph83

**(+j ``8qU`.

t7

/

i'

@HihX

Nq(-*]

{qt,].

Jk..(

i,r`lr

Trkks

{*]'*

x(i), x()

,

,H("X/ ..,

y(.-|)

;(i),

x(Hr/

"

,

x(t),

(7h

,,,,

p-

Y`

#

i".

((HX

1 Ur,",u

4>I

M-z

Y.'`im

+

j

],]

N-

xtm)

m1|

]1

I -XYr'N-N/

m

lv,]

*QJ-

m

iNN

-N

3r

,XN

1

?r

.

-

x

(e)

k'

H

,

Hr.=

*>5

+

h'c I

M'h

Hk

R(u)1

R(]h

w"

m--,

.

(#

7

rrH

+

,H

N

t 4

-

rH

-r'@

x(z-r+h)

w,h

r1i

kNm;

1

G

-+c

Hk

l'v

XX-'t]*-.-./

/],

'M;

m

-Y ?r+- -

rN.hi;

\

Nt

,

`im

l

-

;4..h+

?r

l

-'YM

,/'Y.`

9r

?.r

|,

l'

`z,

X .,,

Hr,

r/,

4 )

+

Hh

)

'+

.

?

xN

h

it

,

7.

7

H*,

t

qqq

Documents

Sayısal İşaret İşleme - Gebze Teknik Üniversitesi Yrd. Doç. Dr. Köksal HOCAOĞLU Ders Notu