Matlab设计数字滤波器入门

一个3阶低通滤波器由下面差分方程描述：

y(n) = 0.0181 x(n) + 0.0543 x(n-1) + 0.0543 x(n-2) + 0.0181 x(n-3) + 1.76 y(n-1) - 1.1829 y(n-2) + 0.2781 y(n-3)

画出这个滤波器的幅度和相位响应，并验证它是一个低通滤波器。
代码1：

clear
close all
 
b = [0.0181,0.0543,0.0543,0.0181];
a = [1.0000,-1.7600,1.1829,-0.2781];
[h,t]=impz(b,a);
k = [0:500];
w = (pi/500)*k;
t = t';
h = h';
H = h * ( exp(-j*pi/500) ).^(t'*k);
magH = abs(H);
angH = angle(H);
subplot(2,1,1);
plot(w/pi,magH);
title('Magnitude part');
subplot(2,1,2);
plot(w/pi,angH);
title('Angle part');

这种方法的思路是通过差分方程可以得到有理传递函数或者频率响应的分子和分母系数，通过impz函数得到脉冲响应，之后由脉冲响应h(n)得到频率响应
代码二：

clc
clear
close all
 
b = [0.0181,0.0543,0.0543,0.0181];
a = [1.0000,-1.7600,1.1829,-0.2781];
m = 0:length(b)-1;
l = 0:length(a)-1;
k = 0:500;
w = (pi/500)*k;
nume = b * exp(-j * m' * w);
den = a * exp(-j * l' * w);
H = nume ./ den;
magH = abs(H);
angH = angle(H);
 
subplot(2,1,1);
plot(w/pi,magH);
title('Magnitude Response');
 
subplot(2,1,2);
plot(w/pi,angH);
title('Phase Response');