IIR數(shù)字濾波器設計及應用

1、YUNNAN NORMAL UNIVERSITY本科學生驗證性實驗報告學號 114090315 姓名 李開斌學院物電學院專業(yè)、班級 11電子實驗課程名稱 數(shù)字信號處理教師及職稱李宏寧開課學期2013至2014學年 下 學期填報時間2014 年 5 月 14 日云南師范大學教務處編印H(z)aiz i實驗設計方案實驗序號09實驗名稱IIR數(shù)字濾波器設計及應用實驗時間2014年5月14日實驗室同析3棟3131.實驗目的2.加深理解IIR數(shù)字濾波器的特性，掌握IIR數(shù)字濾波器的設計原理與設計方法, 以及IIR數(shù)字濾波器的應用。(2)調(diào)用butter函數(shù)設計出巴特沃斯濾波器，格式為 b,a = but

2、ter(N,Wc,options) 輸入?yún)?shù)：N和Wc是buttord函數(shù)返回的參數(shù)，含義見上。Options= ' low' , ' high ' , ' bandphSS對應彳氐通top1通,、帶通、帶阻，默認情況下為低通或帶通。輸出參數(shù)：b和a為設計出的IIR數(shù)字濾波器H(s)的分子多項式和分母多項式的 系數(shù)矩陣。2. (1) Chebyshev I型濾波器設計Chebyshev I型濾波器為通帶紋波控制器：在通帶呈現(xiàn)紋波特性，在阻帶單調(diào)衰減。N,Wc = cheb1ord(Wp, Ws, Ap, As)b,a = cheby1(N,Ap,Wc,o

3、ptions)參數(shù)含義與butter中參數(shù)一致。3. (2) Chebyshev II型濾波器設計Chebyshev II型濾波器為阻帶紋波控制器：在阻帶呈現(xiàn)紋波特性。N,Wc = cheb20rd(Wp, Ws, Ap, As)b,a = cheby2(N,As,Wc,options)4. 橢圓濾波器設計橢圓濾波器在通阻帶都呈現(xiàn)紋波特性。N,Wc = ellipord(Wp,Ws,Ap,As)b,a = ellip(N,Ap,As,Wc,options)利用Matlab中的函數(shù)分析并繪出常用基本信號的波形。注意事項：(1)在使用MATLAB時應注意中英輸入法的切換，在中文輸入法輸入程序時得

4、到的程序是錯誤的；(2) MATLAB中兩個信號相乘表示為x.*u,中間有個.，同樣兩個信號相除也 是如此；(3)使用MATLAB編寫程序時，應新建一個m文件，而不是直接在Comandante 窗口下編寫程序；在使用MATLAB編程時，應該養(yǎng)成良好的編寫習慣。5.實驗數(shù)據(jù)處理方法比較法畫圖法1.實驗現(xiàn)象與結果 21 .信號 xk 1 cos(-k) cos(k),確定設計指標，實現(xiàn)各種IIR數(shù)字濾波器 43以實現(xiàn)以下信號處理。2 .(1)設計IIR低通濾波器，濾除 cos(k)的成分。3%低通濾波器N,Wc=buttord(0.250,0.677,3,60)b,a=butter(N,Wc,&#

5、39;low')freqz(b,a);axis(0,1,-120,0);grid ontitle('巴特沃斯低通數(shù)字濾波器')0.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)0.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)N =5 W© =0.2702 b =0.00450.02260.04520. ()1520.02260.0045a =L 0000-2,27292. 4660T, 43590. 4450-0

6、. 0575(2)設計IIR圖通濾波器，濾除 1 cos(-k)的成分4%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')-50-100巴特沃斯高通數(shù)字濾波器00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)200IseorngsT esaB0-20000.10.20.30.40.50.60.70.80.91No

7、rmalized Frequency ( rad/sample)-400N -EWc =d 272 b =0. 2399T, 19962.3992-2.39921. 1y95-0. 2399a =L 0000-2- 27292.46601.43590.4450-0. 05752.(3)設計IIR帶通濾波器，濾除 1 cos(k)的成分3%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)

8、;axis(0,1,-120,0);grid ontitle('巴特沃斯帶通數(shù)字濾波器')巴特沃斯帶通數(shù)字濾波器-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)-2000-400000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)-6000N =40 Wc =0.24990.6701b =Columns 1 through 70.00000-0.000000.00000-0.0000Columns 8 throu

9、gh 1400.00000-0.000000.00000Columns 15 through 21-0.000000.00000-0.000100.0003Columns 22 through 280-0.000700.00170-0.00370Columns 29 through 350.00720-0.012500.01950-0.0276Columns 36 through 4200.03530-0.040800.04290Columns 43 through 49-0.040800.03530-0.027600.0195Columns 50 through 560-0.012500.0

10、0720-0.00370Columns 57 through 630.00170-0.000700.00030-0.0001Columns 64 through 7000.00000-0.000000.00000Columns 71 through 77-0.000000.00000-0.000000.0000Columns 78 through 810-0.000000.00001.0e+005 *Columns 1 through 70.0000-0.00010.0003-0.00110.0030-0.00740.0160Columns 8 through 14-0.03180.0585-

11、0.10080.1637-0.25190.3692-0.5174Columns 15 through 210.6952-0.89801.1176-1.34271.5597-1.75421.9125Columns 22 through 28-2.02342.0794-2.07732.0188-1.90981.7596-1.5798Columns 29 through 351.3828-1.18030.9828-0.79850.6332-0.49020.3705Columns 36 through 42-0.27340.1970-0.13860.0953-0.06390.0419-0.0268Co

12、lumns 43 through 490.0167-0.01020.0061Columns 50 through 56 -0.00030.0002-0.0001Columns 57 through 63 0.0000-0.00000.0000Columns 64 through 70 -0.00000.0000-0.0000Columns 71 through 77 0.0000-0.00000.0000Columns 78 through 81 -0.00000.0000-0.00000.00350.00000.00000.00000.00000.00000.0020-0.00000.000

13、0-0.00000.0000-0.00110.0000-0.00000.0000-0.00000.0006-0.00000.0000-0.00000.0000(4)設計IIR帶阻濾波器，濾除cos(_k)4%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=buttord(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')的成分JDWTOXMWkhdaM0

14、0巴特沃斯帶阻數(shù)字濾波器50 -26ONormalized Frequency (rad/sample)0-5000-10000-1500000.10.20.30.40.50.60.7Normalized Frequency (rad/sample)N = 40 Wc =0.24990.6701b =1.0e+005 *Columns 1 through 70.0000-0.00000.0000-0.00000.0000-0.00000.0000Columns 8 through 14-0.00000.0000-0.00000.0000-0.00000.0000-0.0000Columns 1

15、5 through 210.0001-0.00010.0003-0.00070.0015-0.00290.0056Columns 22 through 28-0.01020.0179-0.03050.0502-0.07980.1227-0.1828Columns 29 through 350.2636-0.36860.4998-0.65760.8396-1.04091.2534Columns 36 through 42-1.46601.6661-1.84011.9753-2.06102.0904-2.0610Columns 43 through 491.9753-1.84011.6661-1.

16、46601.2534-1.04090.8396Columns 50 through 56-0.65760.4998-0.36860.2636-0.18280.1227-0.0798Columns 57 through 630.0502-0.03050.0179-0.01020.0056-0.00290.0015Columns 64 through 70-0.00070.0003-0.00010.0001-0.00000.0000-0.0000Columns 71 through 770.0000-0.00000.0000-0.00000.0000-0.00000.0000Columns 78

17、through 81-0.00000.0000-0.00000.00001.0e+005 *Columns 1 through 70.0000-0.00010.0003-0.00110.0030-0.00740.0160Columns 8 through 14-0.03180.0585-0.10080.1637-0.25190.3692-0.5174Columns 15 through 210.6952-0.89801.1176-1.34271.5597-1.75421.9125Columns 22 through 28-2.02342.0794-2.07732.0188-1.90981.75

18、96-1.5798Columns 29 through 351.3828-1.18030.9828-0.79850.6332-0.49020.3705Columns 36 through 42-0.27340.1970-0.13860.0953-0.06390.0419-0.0268Columns 43 through 49 0.0167-0.01020.0061Columns 50 through 56 -0.00030.0002-0.0001Columns 57 through 63 0.0000-0.00000.0000Columns 64 through 70 -0.00000.000

19、0-0.0000Columns 71 through 77 0.0000-0.00000.0000Columns 78 through 81 -0.00000.0000-0.00000.00350.00000.00000.00000.00000.00000.0020-0.00000.0000-0.00000.0000-0.00110.0000-0.00000.0000-0.00000.0006-0.00000.0000-0.00000.00002.某帶通濾波器的設計指標為si 0.2 (rad), p1 0.3 (rad), p2 0.6 (rad),s2 0.72 (rad),Ap 1dB,

20、人 42dB(1)用脈沖響應不變法設計各種濾波器：%脈沖響應不變法設計巴特沃斯帶通模擬濾波器Wp =0.3 0.6; Ws =0.2 0.72;Ap = 2; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As);b,a=butter(N,Wc,'bandpass');freqz(b,a);axis(0,1,-120,0);grid ontitle('脈沖響應不變法巴特沃斯 帶通模擬濾波器');-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample) 0

21、 -500 -1000 -1500LRTeanmaaM00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)%脈沖響應不變法設計巴特沃斯帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72;Ap = 2; As = 42; Fs=1;N,Wc=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)

22、;norm=max(abs(h);a=a/norm;plot(w/pi,20*log10(abs(h)/norm);grid ontitle('脈沖響應不變法巴特沃斯帶通數(shù)字濾波器')%脈沖響應不變法設計切比雪夫1型 帶通模擬濾波器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,Ap,Wc,'bandpass');freqz(b,a);axis(0,1,-120,0);grid ontitle('脈沖響應不變法 切比雪夫1型 帶

23、通模擬濾波器');脈沖響應不變法 切比雪夫1型 帶通數(shù)字濾波器0LRTeanmaaM-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)5000-500-1000 00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)%脈沖響應不變法設計切比雪夫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=cheb

24、y1(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('脈沖響應不變法 切比雪夫1型 帶通數(shù)字濾波器');-50八-100-150-200i-250i-300-350-400-450 00.10.20.30.40.50.60.70.8

25、0.91%脈沖響應不變法設計切比雪夫2型 帶通模擬濾波器Wp =0.3 0.6; Ws =0.2 0.72;Ap = 2; As = 42; Fs=1;N,Wc=cheb20rd(Wp,Ws,Ap,As);b,a=cheby2(N,As,Wc,'bandpass');freqz(b,a);axis(0,1,-120,0);grid ontitle('脈沖響應不變法 切比雪夫2型 帶通模擬濾波器);脈沖響應不變法切比雪夫2型帶通數(shù)字濾波器LRTeanmaaM-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency (

26、 rad/sample) 400 200 0 -200 -40000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)%脈沖響應不變法設計 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 = 2; As = 42; Fs=1;N,Wc=cheb20rd(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=im

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

28、脈沖響應不變法 橢圓 帶通模擬濾波器);脈沖響應不變法橢圓 帶通模擬濾波器LRTeanmaaM00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample) 400 200 0 -200 -400o5 -00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)%脈沖響應不變法設計橢圓型帶通數(shù)字濾波器Wp =0.3 0.6; Ws =0.2 0.72;Ap = 2; As = 42; Fs=1;N,Wc=ellipord(Wp,Ws,Ap,As);b,a=elli

29、p(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('脈沖響應不變法 橢圓 帶通數(shù)字濾波器');(2)用雙線性變換法設計各種濾波器：%雙線性變換法設計巴特沃斯帶通模擬濾波器%下列八個程序中約定WWp為數(shù)字頻率WWp =0.3 0.6; WWs =0.2 0.72;Wp=

30、tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=buttord(Wp,Ws,Ap,As);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);LRTeanmaaM-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample) 1000 0 -1000 -200000.10.20.30.40.50.60.70.80.

31、91Normalized Frequency ( rad/sample)%雙線性變換法設計巴特沃斯帶通數(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=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

32、;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')%雙線性變換法設計 切比雪夫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 = 2; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As);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

33、型 帶通模擬濾波器);雙線性變換法切比雪夫1型帶通模擬濾波器00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)-1000 00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)5000-500%雙線性變換法設計切比雪夫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 = 2; As = 42; Fs=1;N,Wc=cheb1ord(Wp,Ws,Ap,As);b,a

34、=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 切比雪夫1型 帶通數(shù)字濾波器%雙線性變換法設計 切比雪夫2型 帶通模擬濾波器WWp =0.3 0.6; W

35、Ws =0.2 0.72;Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=cheb20rd(Wp,Ws,Ap,As);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);雙線性變換法切比雪夫#型帶通模擬濾波器00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)4002000-20000.10.20.

36、30.40.50.60.70.80.91Normalized Frequency ( rad/sample)-400%雙線性變換法設計 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=cheb20rd(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,

37、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');雙線性變換法切比雪夫3型帶通數(shù)字濾波器111L1hi1 11|100.10.20.30.40.50.60.70.80.91%雙線性變換法設計橢圓帶通模擬濾波器WWp =0.3 0.6; WWs =0.2 0.72;Wp=tan(WWp/2);Ws=tan(WWs/2);Ap = 2; As = 42; Fs=1;N,Wc=ellipord

38、(Wp,Ws,Ap,As);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);雙線性變換法橢圓帶通數(shù)字濾波器-50-10000.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample) 400 200 0 -200 -400LRTeanmaaM00.10.20.30.40.50.60.70.80.91Normalized Frequency ( rad/sample)%雙線性

39、變換法設計橢圓型帶通數(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=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);gr

40、id ontitle('雙線性變換法橢圓帶通數(shù)字濾波器');進行對比：%脈沖響應不變法設計巴特沃斯帶通數(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=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);w=linspace(0,pi,512);norm=max(

41、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=cheb1ord(Wp,Ws,Ap,As);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)

42、;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=cheb20rd(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); norm=max

43、(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);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); n

44、orm=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);%雙線性變換法設計巴特沃斯帶通數(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=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

45、,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);%雙線性變換法設計 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 = 2; As = 42; Fs=1;N,Wc=cheb20rd(Wp,Ws,Ap,As);b,a=cheby1(N,As,Wc,'ba

46、ndpass');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);%雙線性變換法設計 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

47、);Ap = 2; As = 42; Fs=1;N,Wc=cheb20rd(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('切比雪夫2型 帶通數(shù)字');subplot(2,2,4);%

48、雙線性變換法設計橢圓型帶通數(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=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)

49、;grid ontitle('橢圓帶通數(shù)字')；巴特沃斯帶通數(shù)字橢圓帶通數(shù)字3.雙音多頻(dual-tone multifrequency, DTMF)信號的產(chǎn)生及檢測在現(xiàn)代通信系 統(tǒng)中有著廣泛的應用，家用電話、移動電話以及公共程控交換機(PBX)都采用DTMF信號發(fā)送和接收電話撥號號碼。DTMF信號由低頻組和高頻組兩組頻率信號構成，高頻為列，低頻為行。按鍵 電話上每個按鍵都由對應的兩個頻率組成。當按下某個鍵時，所得到的按鍵信號是由相應兩個頻率的正弦信號 Xk=Sin( h k) + Sin( l k), h 2a/ fsam ,L 2 fL / fsam , fsam 8kHz120913361477697123770456852789941*0#DTMF信號可以用IIR數(shù)字濾波器來進行解碼。如圖所示接收到的音頻信號通過低通和高通濾波器。由于 DTMF信號行頻低于列頻，所 以低通和高通可以分離出行和列信息。再通過帶通濾波器，對其輸出的振幅大 小進行判斷，可以確定具體的行頻和列頻。如圖中所