数字巴特沃斯滤波器设计

数字巴特沃斯滤波器设计
这是《信号与系统》课上的题目,原题如下：
试设计一个数字低通滤波器,不仅具有模拟巴特沃斯滤波器的幅度响应,而且具有线性相位响应.用Matlab编程计算具有巴特沃斯幅频响应的线性相位滤波器的单位样值响应,并画出30阶的波形.

1-2基于Butterworth模拟滤波器原型,使用双线性状换设计数字滤波器：各参数值为：通带截止频率Omega=0.2*pi,阻带截止频率Omega=0.3*pi,通带波动值Rp=1dB,阻带波动值Rs=15dB,设Fs=4000Hz.
代码：
wp=0.2*pi;ws=0.3*pi;
Fs=4000;T=1/Fs;
OmegaP=(2/T)*tan(wp/2);
OmegaS=(2/T)*tan(ws/2);
rp=1;rs=15;as=15;
ripple=10^(-rp/20);attn=10^(-rs/20);
[n,wn]=buttord(OmegaP,OmegaS,rp,rs,'s');
[z,p,k]=Buttap(n);
[b,a]=zp2tf(z,p,k);
[bt,at]=lp2lp(b,a,wn);
[b,a]=bilinear(bt,at,Fs);
[db,mag,pha,grd,w]=freqz_m(b,a);
%
%下面绘出各条曲线
subplot(2,2,1);plot(w/pi,mag);title('Magnitude Frequency幅频特性');
xlabel('w(/pi)');ylabel('|H(jw)|');
axis([0,1,0,1.1]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);
set(gca,'YTickMode','manual','YTick',[0 attn ripple 1]);grid
subplot(2,2,2);plot(w/pi,db);title('Magnitude Frequency幅频特性(db)');
xlabel('w(/pi)');ylabel('dB');
axis([0,1,-30,5]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);
set(gca,'YTickMode','manual','YTick',[-60 -as -rp 0]);grid
subplot(2,2,3);plot(w/pi,pha/pi);title('Phase Frequency相频特性');
xlabel('w(/pi)');ylabel('pha(/pi)');
axis([0,1,-1,1]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);grid
subplot(2,2,4);plot(w/pi,grd);title('Group Delay群延时');
xlabel('w(/pi)');ylabel('Sample');
axis([0,1,0,15]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);grid