Matlab 四種IIR濾波器紋波特性對比

測試**：

%filtercompare.m

%對比相同階數時四種iir濾波器的波紋特性
close all;
clear;
clc;
fs = 1000; %hz
%低通濾波器對比
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();
title('同階數(n=8),同截止頻率(f_c=100hz)的低通濾波器對比');
%高通濾波器
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();
title('同階數(n=8),同截止頻率(f_c=400hz)的高通濾波器對比');
%帶通濾波器
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();
title('同階數(n=8),同截止頻率(f_c_1=100hz f_c_2 = 400hz)的帶通濾波器對比');
%帶阻濾波器
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();
title('同階數(n=8),同截止頻率(f_c_1=100hz f_c_2 = 400hz)的帶阻濾波器對比');

高通濾波器

帶通濾波器

帶阻濾波器

驗證結果：

1、巴特沃斯濾波器的通帶和阻帶均是單調製化，頻率響應最為平滑，若通帶邊緣滿足指標要求，則通帶內會有富餘量，並不經濟，更有效的方法是將指標的精度要求均勻分布在通帶或阻帶內，這樣能設計出階數較低的濾波器（意會，意會）；

2、切比雪夫ⅰ型濾波器的幅度特性在通帶範圍內是等波紋的，在阻帶範圍內時單調的；

3、切比雪夫ⅱ型濾波器的幅度特性在阻帶範圍內是等波紋的，在通帶範圍內時單調的；

4、橢圓濾波器的幅度特性在通帶和阻帶範圍內均是等波紋的。

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