1、華北電力大學數字信號處理實驗六一：實驗目的加深明白得IIR數字濾波器的特性,把握IIR數字濾波器的設計原理與設計方法,以及IIR數字濾波器的應用.M二：實驗電理,火獻IiR0敝字濾波器的最統函數曲iz(M1)bMzM1 aiZ-1(Nl)N1 i1azaNiz3nZIIR數字濾波器的設計要緊通過成熟的模擬濾波器設計方法來實現：將數字濾波器設計指標轉換為模擬濾波器設計指標,設計出相應的模擬濾波器H(s),再通過脈沖響應不變法或雙線性變換法得到所需的IIR數字濾波器H(z).IIR數字濾波器設計的重要環節是模擬原型低通濾波器的設計,要緊包括Butterworth>Chebyshev和橢圓等濾

2、波器.MATLAB信號處理工具箱中提供了IIR濾波器設計的函數.IIR濾波器階數選擇buttord-巴特沃斯(Butterworth)濾波器階數選擇.cheblord-切比雪夫(Chebyshev)I型濾波器階數選擇.cheb2ord-切比雪夫(Chebyshev)II型濾波器階數選擇.ellipord-橢圓(Elliptic)濾波器階數選擇.IIR濾波器設計butter-巴特沃斯(Butterworth)濾波器設計chebyl-切比雪夫(Chebyshev)I型濾波器設計cheby2-切比雪夫(Chebyshev)II型濾波器設計ellip-橢圓(Elliptic)濾波器設計maxflat-

3、通用的巴特沃斯(Butterworth)低通濾波器設計yulewalk-Yule-Walker濾波器設計(直截了當數字濾波器設計法)1.Butterworth濾波器設計Butterworth濾波器是通帶、阻帶都單調衰減的濾波器.(1)調用buttord函數確定巴特沃斯濾波器的階數,格式為N,Wc=buttord(Wp,Ws,Ap,As)輸入參數：Ap,As為通帶最大衰減和阻帶最小衰減,以dB為單位.Wp,Ws為歸一化通帶截頻和阻帶截頻,0<Wp,Ws<1.輸出參數：N為濾波器的階數；Wc為截頻,0<Wc<1.(2)調用butter函數設計出巴特沃斯濾波器,格式為b,a=

4、butter(N,Wc,options)輸入參數：N和Wc是buttord函數返回的參數,含義見上.Options='low','high','bandpass,'stop',分不對應低通、高通、帶通、帶阻,默認情形下為低通或帶通.輸出參數：b和a為設計出的IIR數字濾波器H(s)的分子多項式和分母多項式的系數矩陣.2. ChebyshevI型濾波器設計ChebyshevI型濾波器為通帶紋波操縱器：在通帶出現紋波特性,在阻帶單調衰減.N,Wc=cheb1ord(Wp,Ws,Ap,As)b,a=cheby1(N,Ap,Wc,options)

5、參數含義與butter中參數一致.3. ChebyshevII型濾波器設計ChebyshevII型濾波器為阻帶紋波操縱器：在阻帶出現紋波特性.N,Wc=cheb2ord(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出現紋波特性.N,Wc=ellipord(Wp,Ws,Ap,As)b,a=ellip(N,Ap,As,Wc,options)£.ixe£,0.11ziwinserx;xoqjlsue寫kiqpuinao*口e,pCvud±idViihduTog«-tstar-te-d,s

6、electMAfLAfiU三口r&eji二三ftmmtKeHelpne-ni-L-Ilieelenenttypje壯必白眄njst&1eruinatedbyths1112fteKingsnef-tnane>*.ConLdr.iotp：iicwthefile:ci1ab*tcjdIIiOjcccsiiiucccsLiiL£ijifo.zjlL口濾波三：實驗內容1-(1)IoqLeHeslrtop也ind口*Help7,3,60)統函數凹回區呼乘M端人以國a門工要口題axis(0,1,-120,0);巴特沃斯高通數字濾波器gridon世屆'國持沃痂征通數字漕

7、波器=JB(2)N,Wc=buttord(0.250,0.677,3,60)b,a=butter(N,Wc,'high')freqz(b,a);axis(0,1,-120,0);3992-2.3892L1Q96-Q-239Bgridon“title('巴特沃斯高通數字濾波器')1 .COCO-2,2r292.40150:“心曬0.4450-0.0575>d(3)Wp=0.250.67;Ws=0.25-0.030.67+0.03;Rp=3;Rs=60;N,Wc=buttord(Wp,Ws,Rp,Rs)b,a=butter(N,Wc,'bandpass

8、')freqz(b,a);axis(0,1,-120,0);gridon40Wc=0.24990.6701Columnsthrough90.00000-0.00000.0000-0.00000.0000Columns10through180-0.00000.00000.0000-0.0000Columns19through27-0.00010.001700.00030-0.0037-0.0007Columns28through360.0072-0.01250.01950-0.0276Columns37through450.0353-0.04080.0429-0.04080.0353Co

9、lumns46through540-0.02760.0195-0.01250.0072Columns55through63-0.00370.0017-0.00070.00030-0.0001Columns64through720.0000-0.00000.00000-0.0000Columns73through810.00000-0.00000.0000-0.00000.00001.0e+005*Columns1through90.0000-0.00010.0003-0.00110.0030-0.00740.0160-0.03180.0585Columns10through18-0.10080

10、.1637-0.25190.3692-0.51740.69520.89801.1176-1.3427Columns19through271.5597-1.75421.9125-2.02342.0794-2.07732.0188-1.90981.7596Columns28through36-1.57981.3828-1.18030.9828-0.79850.63320.49020.3705-0.27340.19700.0167-0.0102Columns46-0.00350.00010.0000Columns550.00000.0000-0.0000Columns64-0.00000.00000

11、.0000Columns730.00000.0000-0.00000.13860.09530.0061through540.0020-0.0011-0.0000through630.00000.00000.0000through720.0000-0.0000-0.0000through810.00000.00000.0000-0.06390.04190.0006-0.0003-0.00000.00000.0000-0.0000-0.00000.0000-0.02680.0002-0.00000.0000-0.0000>>(4)Wp=0.250.67;Ws=0.25-0.030.67

12、+0.03;Rp=3;Rs=60;-！-'NormalizedFrequencyrad/sample)N,Wc=bugo_rd(Wp,Ws,_RPRS)一b,a=butter(Nf|eqZ(bDa);07080.91axist0,1gridontitle?世震沃加帶阻羲字幕被器4'口5、NormalizedFrequency(xkrad/sample)N=40Wc=0.24990.6701b=1.0e+005*Columns1through70.0000-0.00000.00000.0000Columns8through14-0.00000.0000-0.00000.0000C

13、olumns15through210.0001-0.00010.00030.0056Columns22through28-0.01020.0179-0.03050.1828Columns29through350.2636-0.36860.4998-0.00000.0000-0.00000.0000-0.00000.0000-0.00070.0015-0.00290.0502-0.07980.1227-0.65760.8396-1.04091.2534Columns36through42-1.46601.6661-1.84012.0610Columns43through491.9753-1.84

14、011.66610.8396Columns50through56-0.65760.4998-0.36860.0798Columns57through630.0502-0.03050.01790.0015Columns64through70-0.00070.0003-0.00010.0000Columns71through770.0000-0.00000.00000.0000Columns78through81-0.00000.0000-0.0000a=1.0e+005*Columns1through70.0000-0.00010.00030.0160Columns8through14-0.03

15、180.0585-0.10080.51741.9753-2.06102.0904-1.46601.2534-1.04090.2636-0.18280.1227-0.01020.0056-0.00290.0001-0.00000.0000-0.00000.0000-0.00000.0000-0.00110.0030-0.00740.1637-0.25190.3692Columns15through211.5597-1.7542-1.90981.7596-0.6332-0.4902-0.06390.0419-0.0020-0.0011-0.00000.0000-0.0000-0.0000-0.00

16、000.0000-0.0000-0.00000.6952-0.89801.1176-1.34271.9125Columns22through28- 2.02342.0794-2.07732.01881.5798Columns29through351.3828-1.18030.9828-0.79850.3705Columns36through42- 0.27340.1970-0.13860.09530.0268Columns43through490.0167-0.01020.0061-0.00350.0006Columns50through56- 0.00030.0002-0.00010.000

17、00.0000Columns57through630.0000-0.00000.0000-0.00000.0000Columns64through70- 0.00000.0000-0.00000.00000.0000Columns71through770.0000-0.00000.0000-0.00000.0000Columns78through81- 0.00000.0000-0.00000.0000(5)生成0-9其他贊字的DTMF信號,根據上述方法進行解碼,驗證該方法的正確性.而對干圖中的第一組帶通濾波器的吐輸著分別的函球趟響,畫出幅版響應曲線口同理在一張圖上用不同顏色畫出第二組帶通濾波

18、器的3個輸出的幅頻響應曲線.能否用這種方法解出DTMF信用二(2)N,Wc=buttord(0.1925,0.30225,3,60)b,a=butter(N,Wc)freqz(b,a);axis(0,1,-120,0);gridontitle'巴特沃斯低通數字濾波器'T0=204;N=205;T=1;k=0:T0;x=sin(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);subplot(4,1,1);stem(k,x);N,Wc=buttord(0.1925,0.30225,3,60)b,a=butter(N,Wc,'high'

19、;)freqz(b,a);axis(0,1,-120,0);gridonT0=204;N=205;T=1;k=0:T0;x=sin(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);subplot(4,1,1);stem(k,x);(3)Wp1=680720/4000;Ws1=650-20720+20/4000;Rp1=3;Rs1=40;N1,Wn1=cheb1ord(Wp1,Ws1,Rp1,Rs1);b1,a1=cheby1(N1,Rp1,Wn1);freqz(b1,a1,512,8000);Htle('I型切比雪夫濾波器1');gridonW

20、p2=750790/4000;Ws2=750-20790+20/4000;Rp2=3;Rs2=40;N2,Wn2=cheb1ord(Wp2,Ws2,Rp2,Rs2)b2,a2=cheby1(N2,Rp2,Wn2);figure;freqz(b2,a2,512,8000);title('I型切比雪夫濾波器2');gridonWp3=830870/4000;Ws3=830-20870+20/4000;Rp3=3;Rs3=40;N3,Wn3=cheb1ord(Wp3,Ws3,Rp3,Rs3)b3,a3=cheby1(N3,Rp3,Wn3);figure;freqz(b3,a3,512

21、,8000);title('I型切比雪夫濾波器3');gridonWp4=920960/4000;Ws4=920-20960+20/4000;Rp4=3;Rs4=40;N4,Wn4=cheb1ord(Wp4,Ws4,Rp4,Rs4);b4,a4=cheby1(N4,Rp4,Wn4);figure;nllx4,512,8000);帆風時型切上fi1法微|游企的產品*網目百灰k=0:1:500;.InsertIoolsgdrtQpILindowHelpx=Sfn(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);濾波后?梟輸出曲線y2=filtery

22、3=filtery4=fi1terfigure;,plot(k,y1title('濾號02legend.Q4b2,a2,x);b3,a3,x);(b4,a4,x);Ry2,'gTk,y3gRy4,'y)；玄后4條輸出曲線'""''-r1597HZ','770HZ','852HZ','941OE-08637H7770HZ852HZ941HZ.ii-060100160200250300360JOO450500gridon;Wp2=13101350/4000;Ws2=1310-3013

23、50+30/4000;Rp2=3;Rs2=40;N2,Wn2=cheb1ord(Wp2,Ws2,Rp2,Rs2);b2,a2=cheby1(N2,Rp2,Wn2);figure;freqz(b2,a2,512,8000);title('I型切比雪夫濾波器2');gridon;Wp3=14601500/4000;Ws3=1460-301500+30/4000;Rp3=3;Rs3=40;N3,Wn3=cheb1ord(Wp3,Ws3,Rp3,Rs3)b3,a3=cheby1(N3,Rp3,Wn3);figure;freqz(b3,a3,512,8000);title('I型

24、切比雪夫濾波器3');gridon;k=0:1:500;x=sin(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);y1=filter(b1,a1,x);y2=filter(b2,a2,x);y3=filter(b3,a3,x);figure;plot(k,y1,k,y2,'g-',k,y3,'y-');title('輸出曲線');legend('1209HZ','1336HZ','1477HZ');k=0:1:500;x0=sin(2/8000)*941*

25、pi*k)+sin(2/8000)*1336*pi*k);x1=sin(2/8000)*697*pi*k)+sin(2/8000)*1209*pi*k);x2=sin(2/8000)*697*pi*k)+sin(2/8000)*1336*pi*k);x3=sin(2/8000)*697*pi*k)+sin(2/8000)*1477*pi*k);x4=sin(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);x5=sin(2/8000)*770*pi*k)+sin(2/8000)*1336*pi*k);x6=sin(2/8000)*770*pi*k)+sin(2/

26、8000)*1477*pi*k);x7=sin(2/8000)*852*pi*k)+sin(2/8000)*1209*pi*k);x8=sin(2/8000)*852*pi*k)+sin(2/8000)*1336*pi*k);x9=sin(2/8000)*852*pi*k)+sin(2/8000)*1477*pi*k);Wp1=680720/4000;Ws1=650-20720+20/4000;Rp1=3;Rs1=40;N1,Wn1=cheb1ord(Wp1,Ws1,Rp1,Rs1);B1,A1=cheby1(N1,Rp1,Wn1);Wp2=750790/4000;Ws2=750-20790+

27、20/4000;Rp2=3;Rs2=40;N2,Wn2=cheb1ord(Wp2,Ws2,Rp2,Rs2);B2,A2=cheby1(N2,Rp2,Wn2);Wp3=830870/4000;Ws3=830-20870+20/4000;Rp3=3;Rs3=40;N3,Wn3=cheb1ord(Wp3,Ws3,Rp3,Rs3);B3,A3=cheby1(N3,Rp3,Wn3);Wp4=920960/4000;Ws4=920-20960+20/4000;Rp4=3;Rs4=40;N4,Wn4=cheb1ord(Wp4,Ws4,Rp4,Rs4);B4,A4=cheby1(N4,Rp4,Wn4);wp1

28、=11801220/4000;ws1=1180-301220+30/4000;rp1=3;rs1=40;n1,wn1=cheb1ord(wp1,ws1,rp1,rs1);b1,a1=cheby1(n1,rp1,wn1);wp2=13101350/4000;ws2=1310-301350+30/4000;rp2=3;rs2=40;n2,wn2=cheb1ord(wp2,ws2,rp2,rs2);b2,a2=cheby1(n2,rp2,wn2);wp3=14601500/4000;ws3=1460-301500+30/4000;rp3=3;rs3=40;n3,wn3=cheb1ord(wp3,ws

29、3,rp3,rs3);b3,a3=cheby1(n3,rp3,wn3);Y01=filter(B1,A1,x0);Y02=filter(B2,A2,x0);Y03=filter(B3,A3,x0);Y04=filter(B4,A4,x0);figure;subplot(2,1,1);plot(k,Y01,k,Y02,'y-',k,Y03,'r-',k,Y04,'g-');title('輸出曲線1');legend('697HZ','770HZ','852HZ','941HZ&

30、#39;);subplot(2,1,2);y01=filter(b1,a1,x0);y02=filter(b2,a2,x0);y03=filter(b3,a3,x0);plot(k,y01,k,y02,'g-',k,y03,'r-');Z','1336HZ','1477HZ');1,A1,x1);Heskt叩kndowHelp輸出曲線1I-697HZ770HZB52HZ941HZY12fter(B2;A2x1);'山-plot(k,Y'口三黑)y:ig5-1y11=filtey12=filtey13=fil

31、te-0.5plot(k,y1r(b1,a1,x1);r(b2,a2,x1);箝r(b3,a3,x1);ii12O9HZ133GHZ1477HZ1,k,y12,'y-',k,y13,'g-');111Mlegend('697HZ','770HZ','852HZ','941HZ');!?Y13=filter(B3,A3,x1);Y14=fi檢r(B4,A4,x1);1subplot(2,1,2);legend('1209HZ','1336HZ','1477HZ&

32、#39;);丑1-T0=500;N=501;T=1;k=0:T:T0;x0=sin(2/8000)*941*pi*k)+sin(2/8000)*1336*pi*k);x1=sin(2/8000)*697*pi*k)+sin(2/8000)*1209*pi*k);x2=sin(2/8000)*697*pi*k)+sin(2/8000)*1336*pi*k);x3=sin(2/8000)*697*pi*k)+sin(2/8000)*1477*pi*k);x4=sin(2/8000)*770*pi*k)+sin(2/8000)*1209*pi*k);x5=sin(2/8000)*770*pi*k)+

33、sin(2/8000)*1336*pi*k);x6=sin(2/8000)*770*pi*k)+sin(2/8000)*1477*pi*k);x7=sin(2/8000)*852*pi*k)+sin(2/8000)*1209*pi*k);x8=sin(2/8000)*852*pi*k)+sin(2/8000)*1336*pi*k);x9=sin(2/8000)*852*pi*k)+sin(2/8000)*1477*pi*k);Wp1=680720/4000;Ws1=650-20720+20/4000;Rp1=3;Rs1=40;N1,Wn1=cheb1ord(Wp1,Ws1,Rp1,Rs1);B

34、1,A1=cheby1(N1,Rp1,Wn1);Wp2=750790/4000;Ws2=750-20790+20/4000;Rp2=3;Rs2=40;N2,Wn2=cheb1ord(Wp2,Ws2,Rp2,Rs2);B2,A2=cheby1(N2,Rp2,Wn2);Wp3=830870/4000;Ws3=830-20870+20/4000;Rp3=3;Rs3=40;N3,Wn3=cheb1ord(Wp3,Ws3,Rp3,Rs3);B3,A3=cheby1(N3,Rp3,Wn3);Wp4=920960/4000;Ws4=920-20960+20/4000;Rp4=3;Rs4=40;N4,Wn4=

35、cheb1ord(Wp4,Ws4,Rp4,Rs4);B4,A4=cheby1(N4,Rp4,Wn4);wp1=11801220/4000;ws1=1180-301220+30/4000;rp1=3;rs1=40;n1,wn1=cheb1ord(wp1,ws1,rp1,rs1);b1,a1=cheby1(n1,rp1,wn1);wp2=13101350/4000;ws2=1310-301350+30/4000;rp2=3;rs2=40;n2,wn2=cheb1ord(wp2,ws2,rp2,rs2);b2,a2=cheby1(n2,rp2,wn2);wp3=14601500/4000;ws3=1

36、460-301500+30/4000;rp3=3;rs3=40;n3,wn3=cheb1ord(wp3,ws3,rp3,rs3);b3,a3=cheby1(n3,rp3,wn3);Y01=filter(B1,A1,x0);Y02=filter(B2,A2,x0);Y03=filter(B3,A3,x0);Y04=filter(B4,A4,x0);Ym01=fft(Y01,N)/N;Ym02=fft(Y02,N)/N;Ym03=fft(Y03,N)/N;Ym04=fft(Y04,N)/N;figure;plot(k,abs(fftshift(Ym01),k,abs(fftshift(Ym02),

37、'y-',k,abs(fftshift(Ym03),'g-',k,abs(fftshift(Ym04),'r-');legend('697HZ','770HZ','852HZ','941HZ');title('第一組中"0"濾波后的頻譜')；y01=filter(b1,a1,x0);y02=filter(b2,a2,x0);y03=filter(b3,a3,x0);ym01=fft(y01,N)/N;ym02=fft(y02,N)/N;ym03=f

38、ft(y03,N)/N;figure;plot(k,abs(fftshift(ym01),k,abs(fftshift(ym02),'g-',k,abs(fftshift(ym03),'g-');legend('1209HZ','1336HZ','1477HZ');title('第二組中"0"濾波后的頻譜');Y11=filter(B1,A1,x1);Y12=filter(B2,A2,x1);Y13=filter(B3,A3,x1);Y14=filter(B4,A4,x1);Ym11=fft(Y11,N)/N;Ym12=fft(Y12,N)/N;Ym13=fft(Y13,N)/N;Ym14=fft(Y14,N)/N;figure;plot(k,abs(fftshift(Y