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1、實(shí)驗(yàn)七 IIR數(shù)字濾波器設(shè)計(jì)及應(yīng)用一、實(shí)驗(yàn)?zāi)康?加深理解IIR數(shù)字濾波器的特性，掌握IIR數(shù)字濾波器的設(shè)計(jì)原理與設(shè)計(jì)方法，以及IIR數(shù)字濾波器的應(yīng)用。二、實(shí)驗(yàn)原理 N階IIR數(shù)字濾波器的系統(tǒng)函數(shù)為: IIR數(shù)字濾波器的設(shè)計(jì)主要通過(guò)成熟的模擬濾波器設(shè)計(jì)方法來(lái)實(shí)現(xiàn)：將數(shù)字濾波器設(shè)計(jì)指標(biāo)轉(zhuǎn)換為模擬濾波器設(shè)計(jì)指標(biāo)，設(shè)計(jì)出相應(yīng)的模擬濾波器H(s)，再經(jīng)過(guò)脈沖響應(yīng)不變法或雙線性變換法得到所需的IIR數(shù)字濾波器H(z)。IIR數(shù)字濾波器設(shè)計(jì)的重要環(huán)節(jié)是模擬原型低通濾波器的設(shè)計(jì)，主要包括Butterworth、Chebyshev和橢圓等濾波器。三、實(shí)驗(yàn)內(nèi)容1.信號(hào) ,確定設(shè)計(jì)指標(biāo)，實(shí)現(xiàn)各種IIR數(shù)字濾波器以實(shí)

2、現(xiàn)以下信號(hào)處理。（1）設(shè)計(jì)IIR低通濾波器，濾除 的成分。（2）設(shè)計(jì)IIR高通濾波器，濾除 的成分。（3）設(shè)計(jì)IIR帶通濾波器，濾除 的成分。（4）設(shè)計(jì)IIR帶阻濾波器，濾除 的成分。 要求利用butterord函數(shù)求解濾波器的階數(shù)；利用butter函數(shù)設(shè)計(jì)各IIR數(shù)字濾波器；畫(huà)出濾波器的幅度相應(yīng)和相位響應(yīng)；給出IIR數(shù)字濾波器的系統(tǒng)函數(shù)。N,Wc=buttord(0.250,0.677,3,60)b,a=butter(N,Wc,low)freqz(b,a);axis(0,1,-120,0);grid ontitle(巴特沃斯低通數(shù)字濾波器)N = 5Wc = 0.2702b = 0.0045

3、 0.0226 0.0452 0.0452 0.0226 0.0045a = 1.0000 -2.2729 2.4660 -1.4359 0.4450 -0.0575%高通濾波器N,Wc=buttord(0.250,0.677,3,60)b,a=butter(N,Wc,high)freqz(b,a);axis(0,1,-120,0);grid ontitle(巴特沃斯高通數(shù)字濾波器)N = 5Wc = 0.2702b = 0.2399 -1.1996 2.3992 -2.3992 1.1996 -0.2399a = 1.0000 -2.2729 2.4660 -1.4359 0.4450 -0

4、.0575%帶通濾波器Wp =0.25 0.67; Ws =0.25-0.03 0.67+0.03; Rp = 3; Rs = 60;N,Wc=buttord(Wp,Ws,Rp,Rs)b,a=butter(N,Wc,bandpass)freqz(b,a);axis(0,1,-120,0);grid ontitle(巴特沃斯帶通數(shù)字濾波器)N = 40Wc = 0.2499 0.6701b = Columns 1 through 7 0.0000 0 -0.0000 0 0.0000 0 -0.0000 Columns 8 through 14 0 0.0000 0 -0.0000 0 0.00

5、00 0 Columns 15 through 21 -0.0000 0 0.0000 0 -0.0001 0 0.0003 Columns 22 through 28 0 -0.0007 0 0.0017 0 -0.0037 0 Columns 29 through 35 0.0072 0 -0.0125 0 0.0195 0 -0.0276 Columns 36 through 42 0 0.0353 0 -0.0408 0 0.0429 0 Columns 43 through 49 -0.0408 0 0.0353 0 -0.0276 0 0.0195 Columns 50 throu

6、gh 56 0 -0.0125 0 0.0072 0 -0.0037 0 Columns 57 through 63 0.0017 0 -0.0007 0 0.0003 0 -0.0001 Columns 64 through 70 0 0.0000 0 -0.0000 0 0.0000 0 Columns 71 through 77 -0.0000 0 0.0000 0 -0.0000 0 0.0000 Columns 78 through 81 0 -0.0000 0 0.0000a = 1.0e+005 * Columns 1 through 7 0.0000 -0.0001 0.000

7、3 -0.0011 0.0030 -0.0074 0.0160 Columns 8 through 14 -0.0318 0.0585 -0.1008 0.1637 -0.2519 0.3692 -0.5174 Columns 15 through 21 0.6952 -0.8980 1.1176 -1.3427 1.5597 -1.7542 1.9125 Columns 22 through 28 -2.0234 2.0794 -2.0773 2.0188 -1.9098 1.7596 -1.5798 Columns 29 through 35 1.3828 -1.1803 0.9828 -

8、0.7985 0.6332 -0.4902 0.3705 Columns 36 through 42 -0.2734 0.1970 -0.1386 0.0953 -0.0639 0.0419 -0.0268 Columns 43 through 49 0.0167 -0.0102 0.0061 -0.0035 0.0020 -0.0011 0.0006 Columns 50 through 56 -0.0003 0.0002 -0.0001 0.0000 -0.0000 0.0000 -0.0000 Columns 57 through 63 0.0000 -0.0000 0.0000 -0.

9、0000 0.0000 -0.0000 0.0000 Columns 64 through 70 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 Columns 71 through 77 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 Columns 78 through 81 -0.0000 0.0000 -0.0000 0.0000%帶阻濾波器Wp =0.25 0.67; Ws =0.25-0.03 0.67+0.03; Rp = 3; Rs = 60;N,Wc=buttor

10、d(Wp,Ws,Rp,Rs)b,a=butter(N,Wc,stop)freqz(b,a);axis(0,1,-120,0);grid ontitle(巴特沃斯帶阻數(shù)字濾波器) N = 40Wc = 0.2499 0.6701b = 1.0e+005 * Columns 1 through 7 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 Columns 8 through 14 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 Columns 15 through 21 0.00

11、01 -0.0001 0.0003 -0.0007 0.0015 -0.0029 0.0056 Columns 22 through 28 -0.0102 0.0179 -0.0305 0.0502 -0.0798 0.1227 -0.1828 Columns 29 through 35 0.2636 -0.3686 0.4998 -0.6576 0.8396 -1.0409 1.2534 Columns 36 through 42 -1.4660 1.6661 -1.8401 1.9753 -2.0610 2.0904 -2.0610 Columns 43 through 49 1.9753

12、 -1.8401 1.6661 -1.4660 1.2534 -1.0409 0.8396 Columns 50 through 56 -0.6576 0.4998 -0.3686 0.2636 -0.1828 0.1227 -0.0798 Columns 57 through 63 0.0502 -0.0305 0.0179 -0.0102 0.0056 -0.0029 0.0015 Columns 64 through 70 -0.0007 0.0003 -0.0001 0.0001 -0.0000 0.0000 -0.0000 Columns 71 through 77 0.0000 -

13、0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 Columns 78 through 81 -0.0000 0.0000 -0.0000 0.0000a = 1.0e+005 * Columns 1 through 7 0.0000 -0.0001 0.0003 -0.0011 0.0030 -0.0074 0.0160 Columns 8 through 14 -0.0318 0.0585 -0.1008 0.1637 -0.2519 0.3692 -0.5174 Columns 15 through 21 0.6952 -0.8980 1.1176

14、-1.3427 1.5597 -1.7542 1.9125 Columns 22 through 28 -2.0234 2.0794 -2.0773 2.0188 -1.9098 1.7596 -1.5798 Columns 29 through 35 1.3828 -1.1803 0.9828 -0.7985 0.6332 -0.4902 0.3705 Columns 36 through 42 -0.2734 0.1970 -0.1386 0.0953 -0.0639 0.0419 -0.0268 Columns 43 through 49 0.0167 -0.0102 0.0061 -0

15、.0035 0.0020 -0.0011 0.0006 Columns 50 through 56 -0.0003 0.0002 -0.0001 0.0000 -0.0000 0.0000 -0.0000 Columns 57 through 63 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 Columns 64 through 70 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 Columns 71 through 77 0.0000 -0.0000 0.0000 -0.0

16、000 0.0000 -0.0000 0.0000 Columns 78 through 81 -0.0000 0.0000 -0.0000 0.0000實(shí)驗(yàn)內(nèi)容2(1) 用脈沖響應(yīng)不變法設(shè)計(jì)各種濾波器：%脈沖響應(yīng)不變法設(shè)計(jì) 巴特沃斯 帶通模擬濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As ,s);b,a=butter(N,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(脈沖響應(yīng)不變法 巴特沃斯 帶通模擬濾波器);%脈沖響應(yīng)不變法

17、設(shè)計(jì) 巴特沃斯 帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As);b,a=butter(N,Wc,bandpass); w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(脈沖響應(yīng)不變法 巴特沃斯 帶通數(shù)字濾波器) %脈沖響應(yīng)不變法設(shè)計(jì)

18、切比雪夫1型 帶通模擬濾波器Wp =0.3 0.6;Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As ,s);b,a=cheby1(N,Ap,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(脈沖響應(yīng)不變法 切比雪夫1型 帶通模擬濾波器);%脈沖響應(yīng)不變法設(shè)計(jì) 切比雪夫1型 帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 2; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As);b,a=cheby1(N,

19、As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(脈沖響應(yīng)不變法 切比雪夫1型 帶通數(shù)字濾波器); %脈沖響應(yīng)不變法設(shè)計(jì) 切比雪夫2型 帶通模擬濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=cheb2ord(

20、Wp,Ws,Ap,As ,s);b,a=cheby2(N,As,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(脈沖響應(yīng)不變法 切比雪夫2型 帶通模擬濾波器);%脈沖響應(yīng)不變法設(shè)計(jì) 切比雪夫2型 帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=cheb2ord(Wp,Ws,Ap,As, s);b,a=cheby2(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd

21、,dend=impinvar(b,a,Fs);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(脈沖響應(yīng)不變法 切比雪夫2型 帶通數(shù)字濾波器); %脈沖響應(yīng)不變法設(shè)計(jì) 橢圓 帶通模擬濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As ,s);b,a=ellip(N,Ap,As,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(脈沖響應(yīng)不變法 橢圓

22、 帶通模擬濾波器);%脈沖響應(yīng)不變法設(shè)計(jì) 橢圓 型帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72; Ap = 1; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As);b,a=ellip(N,Ap,As,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(脈沖響應(yīng)不變法 橢圓

23、帶通數(shù)字濾波器); (2) 用雙線性變換法設(shè)計(jì)各種濾波器：%雙線性變換法設(shè)計(jì) 巴特沃斯 帶通模擬濾波器%下列八個(gè)程序中約定WWp為數(shù)字頻率WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 1; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As ,s);b,a=butter(N,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(雙線性變換法 巴特沃斯 帶通模擬濾波器);%雙線性變換法設(shè)計(jì)巴特沃斯 帶通數(shù)字濾波器WWp =0.3 0.6;

24、WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 1; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As);b,a=butter(N,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(雙線性變換法 巴特沃斯 帶通數(shù)字濾波器) %雙線性變換法設(shè)計(jì) 切比

25、雪夫1型 帶通模擬濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 1; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As ,s);b,a=cheby1(N,Ap,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(雙線性變換法 切比雪夫1型 帶通模擬濾波器);%雙線性變換法設(shè)計(jì) 切比雪夫1型 帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap =

26、1; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As ,s);b,a=cheby1(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(雙線性變換法 切比雪夫1型 帶通數(shù)字濾波器); %雙線性變換法設(shè)計(jì) 切比雪夫2型 帶通模擬濾波器WWp =

27、0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=cheb2ord(Wp,Ws,Ap,As ,s);b,a=cheby2(N,As,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(雙線性變換法 切比雪夫2型 帶通模擬濾波器);%雙線性變換法設(shè)計(jì) 切比雪夫2型 帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;

28、N,Wc=cheb2ord(Wp,Ws,Ap,As);b,a=cheby2(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(雙線性變換法 切比雪夫2型 帶通數(shù)字濾波器); %雙線性變換法設(shè)計(jì) 橢圓 帶通模擬濾波器WWp =0.3 0.6; WWs =0.2 0.72;W

29、p=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As ,s);b,a=ellip(N,Ap,As,Wc,bandpass);freqz(b,a);axis(0,1,-120,0);grid ontitle(雙線性變換法 橢圓 帶通模擬濾波器);%雙線性變換法設(shè)計(jì) 橢圓 型帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As);b,a

30、=ellip(N,Ap,As,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(雙線性變換法 橢圓 帶通數(shù)字濾波器); (3) 進(jìn)行對(duì)比：%脈沖響應(yīng)不變法設(shè)計(jì) 巴特沃斯 帶通數(shù)字濾波器subplot(2,2,1);Wp =0.3 0.6; Ws =0.2 0.72; Ap = 2; As = 42; Fs=1;N,Wc=b

31、uttord(Wp,Ws,Ap,As ,s);b,a=butter(N,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle( 巴特沃斯 帶通數(shù)字)subplot(2,2,2);Wp =0.3 0.6; Ws =0.2 0.72; Ap = 2; As = 42; Fs=1;N,Wc=

32、cheb1ord(Wp,Ws,Ap,As ,s);b,a=cheby1(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(切比雪夫1型 帶通數(shù)字);subplot(2,2,3);Wp =0.3 0.6; Ws =0.2 0.72; Ap = 2; As = 42; Fs=1;N,Wc=cheb2ord(Wp,Ws

33、,Ap,As ,s);b,a=cheby2(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(切比雪夫2型 帶通數(shù)字);subplot(2,2,4);Wp =0.3 0.6; Ws =0.2 0.72; Ap = 2; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As ,s);b,a

34、=ellip(N,Ap,As,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(橢圓 帶通數(shù)字);subplot(2,2,1);%雙線性變換法設(shè)計(jì)巴特沃斯 帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=

35、1;N,Wc=buttord(Wp,Ws,Ap,As ,s);b,a=butter(N,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(巴特沃斯 帶通數(shù)字)subplot(2,2,2);%雙線性變換法設(shè)計(jì) 切比雪夫1型 帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);W

36、s=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=cheb2ord(Wp,Ws,Ap,As ,s);b,a=cheby1(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle(切比雪夫1型 帶通數(shù)字);subplot(2,2,3);%雙線性變換法

37、設(shè)計(jì) 切比雪夫2型 帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=cheb2ord(Wp,Ws,Ap,As ,s);b,a=cheby2(N,As,Wc,bandpass);w=linspace(0,pi,512);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(

38、abs(h)/norm);grid ontitle(切比雪夫2型 帶通數(shù)字);subplot(2,2,4);%雙線性變換法設(shè)計(jì) 橢圓 型帶通數(shù)字濾波器WWp =0.3 0.6; WWs =0.2 0.72; Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As ,s);b,a=ellip(N,Ap,As,Wc,bandpass);h=freqz(b,a,w);axis(0,1,-120,0);numd,dend=impinvar(b,a,Fs);w=linspace(0,pi,512);norm=max(abs(h);a=a/norm;plot(w/pi,

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