用双线性变换法设计切比雪夫II型的数字IIR带通滤波器5页

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，画出并分析滤波器传输函数的零极点；信号经过该滤波器，其中450Hz，600Hz，滤波器的输出是什么？用Matlab验证你的结论并给出的图形。Matlab 详细设计：% Design of a Cheb II Bandpass Digital Filter by using bilinear metho

2、dclc;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*OmegaP1_2/Fp; Ws1=2*pi*OmegaS1_1/Fp; Ws2=2*pi*OmegaS1_2/Fp; OmegaP1=2*Fp*tan(Wp1/2); % nonline

3、arlizationOmegaP2=2*Fp*tan(Wp2/2); % nonlinearlizationOmegaS1=2*Fp*tan(Ws1/2); % nonlinearlizationOmegaS2=2*Fp*tan(Ws2/2); % nonlinearlizationOmegaP0=sqrt(OmegaP1*OmegaP2);% equivalent mid frequencyBw=OmegaP2-OmegaP1; % bandwithEta_P0=OmegaP0/Bw; % NormalizationEta_P1=OmegaP1/Bw; % NormalizationEta_

4、P2=OmegaP2/Bw; % NormalizationEta_S1=OmegaS1/Bw; % NormalizationEta_S2=OmegaS2/Bw; % NormalizationLemta_P_EquivalentLowPass=Eta_P2/(Eta_P22-Eta_P02); % change to the equivalent Lowpass patameterLemta_S1_EquivalentLowPass=-Eta_S1/(Eta_S12-Eta_P02); % change to the equivalent Lowpass patameterLemta_S2

5、_EquivalentLowPass=Eta_S2/(Eta_S22-Eta_P02); % change to the equivalent Lowpass patameterLemta_S_EquivalentLowPass=min(Lemta_S1_EquivalentLowPass,Lemta_S2_EquivalentLowPass); % get the smallest % Estimate the Filter OrderN, Wn=cheb2ord(Lemta_P_EquivalentLowPass, Lemta_S_EquivalentLowPass, Rp, Rs,s);

6、 % Design the Filternum1,den1=cheby2(N,Rs,Wn,s); num2,den2=lp2bp(num1,den1,OmegaP0,Bw);num,den=bilinear(num2,den2,Fp);% Compute the gain responsew = 0:pi/255:pi;h = freqz(num,den,w);g = 20*log10(abs(h);% Plot the gain responsefigure;plot(w/pi,g);grid axis(0 1 -60 5);xlabel(omega /pi); ylabel(Gain in

7、 dB);title(Gain Response of a Cheb II Bandpass Filter);%Plot the poles and zerosz,p,k=tf2zp(num,den);figure;zplane(z,p); %title()f1=450;f2=600;t=0:0.0001:1x1=sin(2*pi*f1*t);x2=sin(2*pi*f2*t);x=x1+x2;figure;subplot(2,2,1)%x1plot(x1);grid on;axis(0,50*pi,-3,3);xlabel(t);ylabel(x1(t);title(x1);subplot(2,2,2)%x1plot(x2);grid on;axis(0,50*pi,-3,3);xlabel(t);ylabel(x2(t);title(x2);subplot(2,2,3)%xplot(x);grid on;axis(0,50*pi,-3,3);xlabel(t);ylabel(x(t);title(x)%X=fft(x);y=filter(