[Matlab]四种IIR滤波器纹波特性对比

Posted 2020-11-11 Alimy

测试代码：

%FilterCompare.m
%对比相同阶数时四种IIR滤波器的波纹特性


close all;
clear;
clc;


fs = 1000; %Hz


%低通滤波器对比
N1 = 8;
wp = 50 / ( fs / 2);
ws = 100 / ( fs / 2);
alpha_p = 1;
alpha_s = 20;

[ b1,a1] = butter( N1 , ws , \'low\' );
[ b2,a2] = cheby1( N1 , alpha_p , ws , \'low\' );
[ b3,a3] = cheby2( N1 , alpha_s , ws , \'low\' );
[ b4,a4] = ellip ( N1 , alpha_p,alpha_s , ws , \'low\' );



[H1,w1] = freqz(b1,a1,1024*4);
[H2,w2] = freqz(b2,a2,1024*4);
[H3,w3] = freqz(b3,a3,1024*4);
[H4,w4] = freqz(b4,a4,1024*4);
w1 = w1/pi *fs/2;
w2 = w2/pi *fs/2;
w3 = w3/pi *fs/2;
w4 = w4/pi *fs/2;
figure(1);
plot(w1,abs(H1),\'black\',\'linewidth\',0.5);
hold on;
plot(w2,abs(H2),\'red\',\'linewidth\',0.5);
plot(w3,abs(H3),\'green\',\'linewidth\',0.5);
plot(w4,abs(H4),\'blue\',\'linewidth\',0.5);
xlim([0 500]);
ylim([0 1.1]);
legend({ \'butter\' , \'cheby1\' , \'cheby2\' , \'ellip\'});
title(\'同阶数(N=8),同截止频率(f_c=100Hz)的低通滤波器对比\');


%高通滤波器
N1 = 8;
wp = 400 / ( fs / 2);
ws = 400 / ( fs / 2);
alpha_p = 1;
alpha_s = 20;
[ b1,a1] = butter( N1 , ws , \'high\' );
[ b2,a2] = cheby1( N1 , alpha_p , ws , \'high\' );
[ b3,a3] = cheby2( N1 , alpha_s , ws , \'high\' );
[ b4,a4] = ellip( N1 , alpha_p,alpha_s , ws , \'high\' );
[H1,w1] = freqz(b1,a1,1024*4);
[H2,w2] = freqz(b2,a2,1024*4);
[H3,w3] = freqz(b3,a3,1024*4);
[H4,w4] = freqz(b4,a4,1024*4);
w1 = w1/pi *fs/2;
w2 = w2/pi *fs/2;
w3 = w3/pi *fs/2;
w4 = w4/pi *fs/2;
figure(2);
plot(w1,abs(H1),\'black\',\'linewidth\',0.5);
hold on;
plot(w2,abs(H2),\'red\',\'linewidth\',0.5);
plot(w3,abs(H3),\'green\',\'linewidth\',0.5);
plot(w4,abs(H4),\'blue\',\'linewidth\',0.5);
xlim([0 500]);
ylim([0 1.1]);
legend({ \'butter\' , \'cheby1\' , \'cheby2\' , \'ellip\'});
title(\'同阶数(N=8),同截止频率(f_c=400Hz)的高通滤波器对比\');



%带通滤波器

N1 = 8;
wp = [ 100 , 400 ] / ( fs / 2);
ws = [ 100 , 400 ] / ( fs / 2);
alpha_p = 1;
alpha_s = 20;
[ b1,a1] = butter( N1 , ws , \'bandpass\' );
[ b2,a2] = cheby1( N1 , alpha_p , ws , \'bandpass\' );
[ b3,a3] = cheby2( N1 , alpha_s , ws , \'bandpass\' );
[ b4,a4] = ellip( N1 , alpha_p,alpha_s , ws , \'bandpass\' );
[H1,w1] = freqz(b1,a1,1024*4);
[H2,w2] = freqz(b2,a2,1024*4);
[H3,w3] = freqz(b3,a3,1024*4);
[H4,w4] = freqz(b4,a4,1024*4);
w1 = w1/pi *fs/2;
w2 = w2/pi *fs/2;
w3 = w3/pi *fs/2;
w4 = w4/pi *fs/2;
figure(3);
plot(w1,abs(H1),\'black\',\'linewidth\',0.5);
hold on;
plot(w2,abs(H2),\'red\',\'linewidth\',0.5);
plot(w3,abs(H3),\'green\',\'linewidth\',0.5);
plot(w4,abs(H4),\'blue\',\'linewidth\',0.5);
xlim([0 500]);
ylim([0 1.1]);
legend({ \'butter\' , \'cheby1\' , \'cheby2\' , \'ellip\'});
title(\'同阶数(N=8),同截止频率(f_c_1=100Hz f_c_2 = 400Hz)的带通滤波器对比\');



%带阻滤波器
N1 = 8;
wp = [ 100 , 400 ] / ( fs / 2);
ws = [ 100 , 400 ] / ( fs / 2);
alpha_p = 1;
alpha_s = 20;
[ b1,a1] = butter( N1 , ws , \'stop\' );
[ b2,a2] = cheby1( N1 , alpha_p , ws , \'stop\' );
[ b3,a3] = cheby2( N1 , alpha_s , ws , \'stop\' );
[ b4,a4] = ellip( N1 , alpha_p,alpha_s , ws , \'stop\' );
[H1,w1] = freqz(b1,a1,1024*4);
[H2,w2] = freqz(b2,a2,1024*4);
[H3,w3] = freqz(b3,a3,1024*4);
[H4,w4] = freqz(b4,a4,1024*4);
w1 = w1/pi *fs/2;
w2 = w2/pi *fs/2;
w3 = w3/pi *fs/2;
w4 = w4/pi *fs/2;
figure(4);
plot(w1,abs(H1),\'black\',\'linewidth\',0.5);
hold on;
plot(w2,abs(H2),\'red\',\'linewidth\',0.5);
plot(w3,abs(H3),\'green\',\'linewidth\',0.5);
plot(w4,abs(H4),\'blue\',\'linewidth\',0.5);
xlim([0 500]);
ylim([0 1.1]);
legend({ \'butter\' , \'cheby1\' , \'cheby2\' , \'ellip\'});
title(\'同阶数(N=8),同截止频率(f_c_1=100Hz f_c_2 = 400Hz)的带阻滤波器对比\');

　　

现象：

低通滤波器

高通滤波器

带通滤波器

带阻滤波器

 

验证结果：

1、巴特沃斯滤波器的通带和阻带均是单调变化，频率响应最为平滑，若通带边缘满足指标要求，则通带内会有富余量，并不经济，更有效的方法是将指标的精度要求均匀分布在通带或阻带内，这样能设计出阶数较低的滤波器（意会，意会）；

2、切比雪夫Ⅰ型滤波器的幅度特性在通带范围内是等波纹的，在阻带范围内时单调的；

3、切比雪夫Ⅱ型滤波器的幅度特性在阻带范围内是等波纹的，在通带范围内时单调的；

4、椭圆滤波器的幅度特性在通带和阻带范围内均是等波纹的。