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1、用双线性变换法设计切比雪夫 II型的数字IIR带通滤波器用双线性变换法设计切比雪夫II型的数字IIR带通滤波器用双线性变换法设计原型低通为切比雪夫II型的数字IIR带通滤波器，要求通带边界频率 为400Hz, 500Hz,阻带边界频率分别为 350Hz, 550Hz,通带最大衰减1dB,阻带最小衰减40dB, 抽样频率为 2000Hz,用 MATLAB 画出幅频特 性，叫出并分析滤波器传输函数的零极点；、一信 号x=Xi+X2=sin(2E)+sin(2*t)经过 该滤波 器，其中f450Hz, f2=600Hz,滤波器的输出y(t) 是什么？用Matlab验症你的结论并给出 x(t),X2
2、(t),x(t), y(t)的图形。Matlab详细设计:% Design of a Cheb II Bandpass Digital Filter by using bilinear method clc;clear all ;Rp = 1;% bandpass attenuation in dBRs = 40;% bandstop attenuation in dBOmegaS1_1=350;OmegaS1_2=550;OmegaP1_1=400;OmegaP1_2=500;Fp=2000;% samling frequencyWp1=2*pi*OmegaP1_1/Fp;Wp2=2*pi*
3、OmegaP1_2/Fp;Ws1=2*pi*OmegaS1_1/Fp;% nonlinearlization% nonlinearlization% nonlinearlization% nonlinearlization% equivalent mid frequencyWs2=2*pi*OmegaS1_2/Fp;OmegaP1=2*Fp*tan(Wp1/2);OmegaP2=2*Fp*tan(Wp2/2);OmegaS1=2*Fp*tan(Ws1/2);OmegaS2=2*Fp*tan(Ws2/2);OmegaP0=sqrt(OmegaP1*OmegaP2);% Normalization
4、% Normalization% Normalization% Normalization% NormalizationBw=OmegaP2-OmegaP1; % bandwithEta_P0=OmegaP0/Bw;Eta_P1=OmegaP1/Bw;Eta_P2=OmegaP2/Bw;Eta_S1=OmegaS1/Bw;% change to theEta_S2=OmegaS2/Bw;Lemta_P_EquivalentLowPass=Eta_P2/(Eta_P2A2-Eta_P0A2); equivalent Lowpass patameterLemta_S1_EquivalentLowP
5、ass=-Eta_S1/(Eta_S1A2-Eta_P0A2);% change to theequivalent Lowpass patameter Lemta_S2_EquivalentLowPass=Eta_S2/(Eta_S2A2-Eta_P0A2);% change to theequivalent Lowpass patameter Lemta_S_EquivalentLowPass=min(Lemta_S1_EquivalentLowPass,Lemta_S2_Equ ivalentLowPass); % get the smallest % Estimate the Filte
6、r OrderN, Wn=cheb20rd(Lemta_P_EquivalentLowPass,Lemta_S_EquivalentLowPass,Rp, Rs, s); % Design the Filter num1,den1=cheby2(N,Rs,Wn,s);num2,den2=lp2bp(num1,den1,OmegaP0,Bw);num,den=bilinear(num2,den2,Fp); % Compute the gain response w = 0:pi/255:pi; h = freqz(num,den,w); g = 20*log10(abs(h); % Plot t
7、he gain response figure; plot(w/pi,g);grid axis(0 1 -60 5);xlabel( omega /pi); ylabel( Gain in dB );title( Gain Response of a Cheb II Bandpass Filter);%Plot the poles and zeros z,p,k=tf2zp(num,den); figure;zplane(z,p);%? ? 6 ?o 6 y & ?心？title( ? 6 ?o 6 y 心？ & ?() ? f1=450;f2=600;t=0:0.0001:1x1=sin(2
8、*pi*f1*t);x2=sin(2*pi*f2*t);x=x1+x2; figure; subplot(2,2,1)%?x1 心?2 - D?plot(x1);gridon;axis(0,50*pi,-3,3);xlabel( t );ylabel( xl(t);title( x1 a?2-D?);subplot(2,2,2)%?x1 心？2 一 D?plot(x2);gridon;axis(0,50*pi,-3,3); xlabel( t );ylabel( x2(t);title( x2 a?2.D?);subplot(2,2,3)%?e ?e ?x ?2 D?plot(x);grido
9、n;axis(0,50*pi,-3,3);xlabel( t );ylabel( x(t);title( e ?e ?D?o?x 心？2 一 D?)%X=fft(x);y=filter(num,den,x);%6 yx ?2 一 ？+ e ?3?subplot(2,2,4);%?e ?3?y 心？2 一 D?plot(real(y);grid on;axis(0,50*pi,-3,3);xlabel( t);ylabel(y);title(?2 ?- e ?3?y 心？2 - D?);测试结果：/* 於 IM gx 海31号制。 。立户 * 匕 A可 ) Mrk H r， A虏 -3+ 1L1
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11、jHa|p 小七-f * znanca a t匕 手;Lcxvi prt iMh-i-LHlI-l ，七匕r t Th* .2丁1*pE 但制1artQij.Eftir41 中 m dpid.m !.#. ,pw* wa+iLirt _&_E(Bill!m,lfli:L mFids-i . .- - -Tftje JUteir 如ULh好MliLFir.laLEwLMrM% Lw兀tqmEiiirtLTBn. Hfi. E r，11tfHlLn 73 jbI II. | O.图三 实验程序截图运行结果如下:Bd n paG0-10-20-30-40-50-600,!1 iihJ 10.10.20.30.40.50.60.70.80.91/ nGain Response of a Cheb II Bandpass Filter-1-0.50.510Real Partx1的波形x2的波形ttt滤波器输出y的波形yt