Bi 1: Trnh by phng php Butterworth thit k b lc s c p ng xung v
hn IIR.B lc butterworth l b lc ch c im cc.Bnh phng p ng bin ca n c
dng nh sau:
Trong N l bc ca b lc. l tn s ct.p ng bin c th c vit di dng
khc:
Trong Ta c bin lc phi nh hn hoc bng 1Do
Ty tng trng hp khc nhau ta c th s dng thng s d, k, A,
K= Ta c
T hm bnh phng bin c th vit nh sau:
Do vy im cc ca b lc nm trn 2N in phn b u trn ng trn bn knh c:
trong k=0,1,2.2N-1Hm truyn ca b lc
T nhng phn tch trn ta c cc bc thit k b lc Butterworth nh sau:Bc
1: Tnh ton thng s k v dBc 2: Xc nh bc ca b lc theo cng thc Bc 3: t
tn s ct trong di
Bc 4: tng hp b lc t cc im cc ca hm nm bn tri mt phng S:
Ta c hm truyn b lc nh sau:
Trong : vi k=0,1,2.2N-1
Bi 2.1 Thit k b lc thng di dng hm fir1 ca Matlab c cc c tnh k
thut sau: tn s ct chun ha 1( theo tiu chun nyquyst) Fc1=0.35;
Fc2=0.65 Di chuyn tip chun ha thp v cao ln lt l 0.1 v 0.15. suy gim
di chn ln lt l 40dB v 50dB cho di chn vng tn s thp v tn s cao. Dao
ng sng hi di thng l 1dB.- Chn hm ca s thch hp. suy gim di chn ln lt
l 40db v 50dB. Dao ng di thng l 1dB.Bng 1: Tnh cht ca tng loi ca
s.windowHm n)vi 0 n N-1 rng di chuyn tip chun ha (F2) suy hao di
chn
Rectangularn)=11.8/N-13dB
Hanning6.2/N-31dB
Hamming6.6/N-43dB
Blackman11/N-58dB
Vi yu cu bi a ra suy gim cc di chn ln lt l 40dB v 50dB do vy ta
chn hm ca s l ca s Blackman.Vi di chuyn tip chun ha l 0.1 cho vng
tn s thp v 0.15 cho vng tn s cao.Do ta tnh c bc ca b lc cn thit k
theo cng thcN==
Thit k b lc trn Matlab.S dng FDAtool thit k.Khi ng Fdatool s c
giao din nh sau:
Hnh 2.1 Giao din FDAtool- Ci t cc thng s ca b lc cn thit k vo
FDAtool.B lc thng di do chn Bandpass. Thit k theo hm fir1. Tc l b
lc fir theo phng php ca s.
t s bc Order l N=111. t cc tn s ct wc1=0.35, wc2=0.65Sau chn
Design filter thit k b lc ta c kt qu nh sau:
Hnh 2.2 Kt qu thit k b lc trn Fdatool- V p ng tn s ca b lc.Xut d
liu ca b lc qua ca s Workspace.Vo file chn export xut d liuTi ca s
comment windows g lnh >>freqz(Hd) v c tnh tn s
Kt qu ta c c tnh tn s nh sau
Hnh 2.3 p ng tn s ca b lcTa c di chuyn tip tn s thp l 0.1 m tn s
ct di tn s thp l 0.35. Do gii hn di chn di tn thp l 0.3. t th p ng
bin hnh 2.3 ta thy rng tn s 0.333 suy gim di chn tn thp l:
-53.93161dB Tha mn yu cu thit k vi suy gim di chn di tn s thp l
40dB.Di chuyn tip vng tn s cao l 0.15 m tn s ct di tn s cao l 0.65
do tn s gii hn ca di chn vng tn s cao l 0.65+0.075=0.735.T th p ng
bin hnh 2.3 ta tht rng tn s 0.666 suy gim di chn l -53dB tha mn yu
cu thit k l t -50dB.
Hnh 2.4 p ng bin ti di thngT hnh 2.4 ta thy dao ng sng hi di
thng nh hn 1dBT nhng iu trn ta thy b lc thit k tha m tt c cc yu cu
m bi ton t ra.Mt s p ng khc:
Hnh 2.5 p ng xung ca b lcHnh 2.6 v tr im cc v im khng ca b
lc
- Xc nh hm truyn t ca b lc:Ta thy rng y l b lc c pha tuyn tnh.
Lc khng quy.Hm truyn t c dng tng qut :
Xc nh hm truyn trn Matlab:Xut vector h s b lc sang workspase
:
Khi ta c kt qu hm truyn ca b lc nh sau:Hz=tf(B,1,1)
Hz = -1.246e-06 z^110 - 7.65e-07 z^109 - 8.604e-06 z^108 -
3.123e-05 z^107 + 6.427e-05 z^106 + 9.554e-05 z^105 - 0.0001052
z^104 - 7.169e-05 z^103 - 1.932e-05 z^102 - 0.0001652 z^101 +
0.00034 z^100 + 0.0004935 z^99 - 0.0005606 z^98 - 0.0004778 z^97 +
0.0002063 z^96 - 0.0002457 z^95 + 0.0008084 z^94 + 0.001351 z^93 -
0.001703 z^92 - 0.001692 z^91 + 0.001199 z^90 + 0.0002071 z^89 +
0.001158 z^88 + 0.002627 z^87 - 0.003822 z^86 - 0.004334 z^85 +
0.003832 z^84 + 0.002174 z^83 + 0.0005013 z^82 + 0.003746 z^81 -
0.006843 z^80 - 0.008941 z^79 + 0.009244 z^78 + 0.00724 z^77 -
0.002896 z^76 + 0.00322 z^75 - 0.009955 z^74 - 0.01574 z^73 +
0.01887 z^72 + 0.01795 z^71 - 0.01225 z^70 - 0.002052 z^69 - 0.0112
z^68 - 0.02497 z^67 + 0.03602 z^66 + 0.04089 z^65 - 0.0366 z^64 -
0.02133 z^63 - 0.005139 z^62 - 0.04109 z^61 + 0.08305 z^60 + 0.1262
z^59 - 0.165 z^58 - 0.1943 z^57 + 0.2101 z^56 + 0.2101 z^55 -
0.1943 z^54 - 0.165 z^53 + 0.1262 z^52 + 0.08305 z^51 - 0.04109
z^50 - 0.005139 z^49 - 0.02133 z^48 - 0.0366 z^47 + 0.04089 z^46 +
0.03602 z^45 - 0.02497 z^44 - 0.0112 z^43 - 0.002052 z^42 - 0.01225
z^41 + 0.01795 z^40 + 0.01887 z^39 - 0.01574 z^38 - 0.009955 z^37 +
0.00322 z^36 - 0.002896 z^35 + 0.00724 z^34 + 0.009244 z^33 -
0.008941 z^32 - 0.006843 z^31 + 0.003746 z^30 + 0.0005013 z^29 +
0.002174 z^28 + 0.003832 z^27 - 0.004334 z^26 - 0.003822 z^25 +
0.002627 z^24 + 0.001158 z^23 + 0.0002071 z^22 + 0.001199 z^21 -
0.001692 z^20 - 0.001703 z^19 + 0.001351 z^18 + 0.0008084 z^17 -
0.0002457 z^16 + 0.0002063 z^15 - 0.0004778 z^14 - 0.0005606 z^13 +
0.0004935 z^12 + 0.00034 z^11 - 0.0001652 z^10 - 1.932e-05 z^9 -
7.169e-05 z^8 - 0.0001052 z^7 + 9.554e-05 z^6 + 6.427e-05 z^5 -
3.123e-05 z^4 - 8.604e-06 z^3 - 7.65e-07 z^2 - 1.246e-06 z
Cu 2.2 Thit k b lc chn di c cng tn s ct v di chuyn tip ging nh
bi 2.1. c suy gim di chn 50dB v dao ng sng hi di thng l 1dB.- Chn
hm ca s thch hp. suy gim di chn l 50dB. Dao ng di thng l 1dB. T bng
1 ta chn c hm ca s l ca s Blackman.- Vi di chuyn tip chun ha l 0.1
cho vng tn s thp v 0.15 cho vng tn s cao.Do ta tnh c bc ca b lc cn
thit k theo cng thcN== 1Tuy nhin do bc ca b lc v bc ca s phi bng
nhau do chn N=112S dng Matlab thit k b lc- khi ng FDAtool ta s thy
xut hin ca s FDAtool nh hnh 2.1Tip theo ta ci t cc thng s ca b lc -
Ci t cc thng s ca b lc cn thit k vo FDAtool.B lc thng di do chn
Bandstop. Thit k theo hm fir1. Tc l b lc fir theo phng php ca
s.
t s bc Order l N=112. t cc tn s ct wc1=0.35, wc2=0.65Sau chn
Design filter thit k b lc ta c kt qu nh sau:
Hnh 2.7 k qu thit k b lc chn 1 di trn fdatool- V p ng tn s ca b
lc.Xut d liu ca b lc qua ca s Workspace.Vo file chn export xut d
liuTi ca s comment windows g lnh >>freqz(Hd) v c tnh tn s
Kt qu ta c c tnh tn s nh sau
Hnh 2.8 p ng tn s ca b lc chn 1 diT p ng tn s hnh 2.8 ta thy rng
suy hao di chn bt u t khong -75dB. Tha mn yu cu v suy hao di chn.
kim tra dao ng di thng ta phng to th ti di thng kt qu nh sau:
Hnh 2.9 p ng bin ti di thngT hnh 2.9 ta thy dao ng sng hi di
thng l rt nh. Tha mn yu cu bi ton l 1dB.
Nh vy b lc thit k tha mn yu cu ca bi ton t ra.Mt s p ng khc ca b
lc:
Hnh 2.10 p ng xung ca b lc
Hnh 2.11 V tr ca cc im cc im khng ca b lc- Xc nh hm truyn t ca b
lcTa thy rng y l b lc c pha tuyn tnh. Lc khng quy.Hm truyn t c dng
tng qut :
Xc nh hm truyn trn Matlab:Xut vector h s b lc sang workspase
:
Khi ta c kt qu hm truyn ca b lc nh sau:Hz=tf(B,1,1)
>> hz=tf(B,1,1)
hz = -2.214e-21 z^111 + 4.146e-06 z^110 + 7.147e-20 z^109 +
3.32e-05 z^108 - 2.462e-19 z^107 - 0.000135 z^106 + 2.392e-18 z^105
+ 0.0001512 z^104 - 1.125e-18 z^103 + 0.0001341 z^102 - 1.207e-18
z^101 - 0.0006452 z^100 + 1.02e-17 z^99 + 0.0008148 z^98 +
1.114e-17 z^97 - 7.583e-18 z^96 + 3.797e-18 z^95 - 0.001617 z^94 +
2.264e-18 z^93 + 0.002576 z^92 + 3.582e-18 z^91 - 0.001113 z^90 +
1.113e-18 z^89 - 0.002767 z^88 + 3.166e-18 z^87 + 0.00607 z^86 +
2.71e-19 z^85 - 0.004544 z^84 + 3.452e-17 z^83 - 0.003011 z^82 +
2.154e-17 z^81 + 0.01158 z^80 + 2.447e-17 z^79 - 0.01223 z^78 +
9.624e-19 z^77 + 3.444e-18 z^76 + 8.809e-17 z^75 + 0.01864 z^74 -
5.923e-19 z^73 - 0.02702 z^72 + 1.097e-16 z^71 + 0.01087 z^70 -
3.894e-17 z^69 + 0.02584 z^68 + 1.289e-16 z^67 - 0.0559 z^66 +
6.559e-17 z^65 + 0.04305 z^64 + 1.954e-17 z^63 + 0.0313 z^62 +
5.375e-17 z^61 - 0.1483 z^60 + 2.743e-17 z^59 + 0.2562 z^58 -
5.544e-17 z^57 + 0.7 z^56 - 5.544e-17 z^55 + 0.2562 z^54 +
2.743e-17 z^53 - 0.1483 z^52 + 5.375e-17 z^51 + 0.0313 z^50 +
1.954e-17 z^49 + 0.04305 z^48 + 6.559e-17 z^47 - 0.0559 z^46 +
1.289e-16 z^45 + 0.02584 z^44 - 3.894e-17 z^43 + 0.01087 z^42 +
1.097e-16 z^41 - 0.02702 z^40 - 5.923e-19 z^39 + 0.01864 z^38 +
8.809e-17 z^37 + 3.444e-18 z^36 + 9.624e-19 z^35 - 0.01223 z^34 +
2.447e-17 z^33 + 0.01158 z^32 + 2.154e-17 z^31 - 0.003011 z^30 +
3.452e-17 z^29 - 0.004544 z^28 + 2.71e-19 z^27 + 0.00607 z^26 +
3.166e-18 z^25 - 0.002767 z^24 + 1.113e-18 z^23 - 0.001113 z^22 +
3.582e-18 z^21 + 0.002576 z^20 + 2.264e-18 z^19 - 0.001617 z^18 +
3.797e-18 z^17 - 7.583e-18 z^16 + 1.114e-17 z^15 + 0.0008148 z^14 +
1.02e-17 z^13 - 0.0006452 z^12 - 1.207e-18 z^11 + 0.0001341 z^10 -
1.125e-18 z^9 + 0.0001512 z^8 + 2.392e-18 z^7 - 0.000135 z^6 -
2.462e-19 z^5 + 3.32e-05 z^4 + 7.147e-20 z^3 + 4.146e-06 z^2 -
2.214e-21z Sample time: 1 secondsDiscrete-time transfer
function.
Bi 2.3 Xy dng b lc fir c pha tuyn tnh thch hp nht c s dng cho lc
thng di v lc chn di trn. - p ng tn s ca cc b lc FIR pha tuyn tnh
Khi h(n) l dy thc th ch cn kho st c tnh tn s H(ej) ca b lc s FIR
pha tuyn tnh trong on [ 0 ] .+ c tnh tn s ca b lc FIR pha tuyn tnh
loi 1 B lc FIR pha tuyn tnh loi 1 c () = - v N l, c tnh tn s l :V N
l nn khai trin biu thc trn thnh tng ca ba thnh phn :
i bin thnh phn th 3, t =>,khi th , khi th :
o chiu ch s v i li bin ca thnh phn th 3 theo n :
V b lc FIR pha tuyn tnh loi 1 c , nn :Trong : Hay : Do
Hay : i bin, t =>,khi th , khi th , nhn c : b
i bin m tr v n, o cn ca tng v thm cos(.0) = 1 vo s hng u :Hay
:Vi cc h s ca chui : v khi Ta c c tnh bin tn s ca b lc FIR pha tuyn
tnhloi 1 :Vi cc h s a(n) ph thuc vo c tnh xung h(n) c tnh pha :
(1.15)Nhn xt : V cos(0) = 1 nn b lc FIR pha tuyn tnhloi 1 khng th
dng lm b lc c H(ej) = 0 ti = 0 , l cc b lc thng cao v di thng (tr
khi b lc c c tnh xung vi ).- c tnh tn s ca b lc FIR pha tuyn tnh
loi 2 B lc FIR pha tuyn tnh loi 2 c () = - v N chn, c tnh tn s l :V
N chn nn khai trin biu thc trn thnh tng ca hai thnh phn :
i bin tng th hai, v bin i tng t nh trn ta nhn c :Vi cc h s :T c
c tnh bin tn s ca b lc FIR pha tuyn tnhloi 2 :Vi cc h s b(n) ph
thuc vo c tnh xung h(n) c tnh pha : Nhn xt : Khi = th vi mi n nn
H(ej)= 0 khi = . Nh vy, b lc FIR pha tuyn tnh loi 2 khng th dng xy
dng b lc c c tnh bin tn s khc 0 ti = , l b lc thng cao v b lc di
chn.. c tnh tn s ca b lc FIR pha tuyn tnh loi 3 B lc FIR pha tuyn
tnh loi 3 c () = - v N l, c tnh tn s l :V N l nn khai trin biu thc
trn thnh tng ca ba thnh phn :
V b lc FIR pha tuyn tnh loi 3 c c tnh xung h(n) phn i xng nn ti
n = (N - 1)/2 th h(n) = 0 . Do biu thc trn c dng :
i bin tng th hai, t m = (N - 1 - n) =>n = (N - 1 - m), nhn c
: i li bin m thnh n v o chiu ch s ca tng th hai :
V b lc FIR pha tuyn tnh loi 3 c , nn :
Tip tc bin i tng t trn , nhn c :Vi cc h s :
T c c tnh bin tn s ca b lc FIR pha tuyn tnh loi 3 :Vi cc h s
c(n) ph thuc vo c tnh xung h(n) c tnh pha :Suy ra :v Nhn xt : Vi =
0 v = th v vi mi n, nn khi H(ej) = 0 . B lc FIR pha tuyn tnh loi 3
khng th dng xy dng b lc c c tnh bin tn s khc 0 ti = 0 v = l cc b lc
thng thp, thng cao v b lc di chn. Nh vy, b lc FIR pha tuyn tnh loi
3 ch xy dng c b lc di thng.c tnh tn s ca b lc FIR pha tuyn tnh loi
4 B lc FIR pha tuyn tnh loi 4 c () = - v N chn, c tnh tn s l : V N
chn nn khai trin biu thc trn thnh tng ca hai thnh phn :
i bin tng th hai, v bin i tng t trn , nhn c : Vi cc h s : T c c
tnh bin tn s ca b lc FIR pha tuyn tnhloi 4 :Vi cc h s d(n) ph thuc
vo c tnh xung h(n) c tnh pha : Suy ra :v Nhn xt: Vi = 0 th , khi
H(ej)= 0 . V th, b lc FIR pha tuyn tnh loi 4 khng th dng xy dng b
lc c c tnh bin tn s khc 0 ti = 0 , l cc b lc thng thp v di chn.Theo
dng c tnh bin tn s H(ej) ca cc b lc s FIR pha tuyn tnh phn tch trn,
rt ra kt lun nh sau :- B lc loi 1 ch lm c cc b lc thng thp v di
chn.- B lc loi 2 ch lm c cc b lc thng thp v di thng.- B lc loi 3 ch
lm c b lc di thng.- B lc loi 4 ch lm c cc b lc thng cao v di
thng.Nh vy vi phn tch trn b lc FIR c pha tuyn tnh thch hp nht c s
dng cho lc thng di l b lc FIR loi 2. V b lc FIR c pha tuyn tnh thch
hp nht c s dng cho lc chn di l FIR loi 1. T cc thit k bi 2.1 v 2.2
ta thy rng chnh l b cc b lc fir loi 2 v loi 1 tng ng.
- Xy dng cu trc cho b lc cho b lc thng diHm truyn t ca b lc thng
di :
Vy S dng cu trc trc tip chun tc ( Direct form FIR
)y(n)x(n)b0+
Z-1
b1+
Z-1
+
b2
Z-1
b(N-1)
Vi cc thng s b lc thit k bi 2.1 ta xy dng b lc trn dsp nh
sau:
L nguyn 12bkt because I love you !
