MATLAB双线性变换法IIR切比雪夫低通数字滤波器的设计

wp=0.2*pi;ws=0.6*pi;rp=3;rs=40;      %数字滤波器指标
Omgp=tan(wp/2)
Omgs=tan(ws/2)        %转化为模拟滤波器指标（K=1）
Fs=0.5;
%模拟原型滤波器计算
[N,wo]=cheb1ord(Omgp,Omgs,rp,rs,'s')%计算阶数N和截止频率wo
[b,a]=cheby1(N,rp,wo,'s')         %求原型滤波器系数b，a
[Ha,Omg]=freqs(b,a);              %求模拟系统频率特性
dbHa=20*log((abs(Ha)+eps)/max(abs(Ha)));%求分贝值，加eps以避开0点
%计算数字滤波器
[bd,ad]=bilinear(b,a,0.5);        %用双线性变换法求数字滤波器系数bd,ad
[H,w]=freqz(bd,ad);                %求数字系统频率特性
dbH=20*log10(abs(H)/max(abs(H)));  %化为分贝值
%画图
subplot(3,2,1),plot(Omg*Omgp/2/pi,dbHa),grid
title('a 模拟幅度响应（dB)');ylabel('幅度/dB');xlabel('f/Hz');
subplot(3,2,2),plot(w/pi,abs(H))
title('b 幅度响应');axis([0,1,0,1]);
subplot(3,2,3),plot(w/pi,dbH),grid
title('c 幅度响应(dB）');axis([0,1,-300,100]);
subplot(3,2,4),plot(w/pi,dbH),grid
title('d 幅度响应(dB）');axis([0,0.7,-60,5]);
subplot(3,2,5),plot(w/pi,angle(H)/pi)
title('e 相位响应');axis([0,1,-1,1]);
subplot(3,2,6),zplane(bd,ad)
title('f 零极图');axis([-1.1,1.1,-1.1,1.1]);
Omgp =

0.3249

Omgs =

1.3764

N =

3

wo =

0.3249

b =

0         0         0    0.0086

a =

1.0000    0.1941    0.0980    0.0086