MATLAB滤波器设计：低通与高通巴特沃斯滤波器实现

%% 设计截止频率为50HZ的6阶巴特沃斯低通滤波器
%[filtered_signal,filtb,filta]=lopass_butterworth(inputsignal,cutoff_freq,Fs,order)
% INPUTS:
% inputsignal = input time series
% cutoff_freq = filter corner frequency
% Fs = data sampling frequency
% order = order of Butterworth filter
% OUTPUTS:
% filtered_signal = the filtered time series
% filtb, filta = filter numerator and denominator (optional)
clear;clc;
t=0:0.005:5;
T=0.005;%时间间隔
Fs=1/T;%采样频率
y1=5*sin(2*pi*10*t)+5*sin(2*pi*60*t);
y2=5*sin(2*pi*10*t);
[filtered_signal,filtb,filta]=lopass_butterworth(y1,50,Fs,6);
figure(1)
subplot(3,1,1)
plot(t,y1)
title('原始信号')
subplot(3,1,2)
plot(t,filtered_signal)
title('滤波后信号')
subplot(3,1,3)
plot(t,y2)
title('5*sin(2*pi*10*t)')
%滤波器的幅频相频曲线
figure(2)
[h,w] = freqz(filtb,filta,256);
%[h,f] = freqz(filtb,filta,256,Fs);
subplot(2,1,1)
plot(w/pi,20*log10(abs(h)))
%plot(f,20*log10(abs(h)))
xlabel('\times\pi')
%xlabel('Hz')
ylabel('gain(dB)')
subplot(2,1,2)
plot(w/pi,angle(h))
%plot(f,angle(h))
xlabel('\times\pi')
%xlabel('Hz')
ylabel('phase (rad)')

%% 设计截止频率为20HZ的6阶巴特沃斯高通滤波器
%[filtered_signal,filtb,filta]=hipass_butterworth(inputsignal,cutoff_freq,Fs,order)
% INPUTS:
% inputsignal = input time series
% cutoff_freq = filter corner frequency
% Fs = data sampling frequency
% order = order of Butterworth filter
% OUTPUTS:
% filtered_signal = the filtered time series
% filtb, filta = filter numerator and denominator (optional)
clear;clc;
t=0:0.01:5;
T=0.01;%时间间隔
Fs=1/T;%采样频率
y1=5*sin(2*pi*10*t)+5*sin(2*pi*30*t);
y2=5*sin(2*pi*30*t);
[filtered_signal,filtb,filta]=hipass_butterworth(y1,20,Fs,6);
figure(1)
subplot(3,1,1)
plot(t,y1)
title('原始信号')
subplot(3,1,2)
plot(t,filtered_signal)
title('滤波后信号')
subplot(3,1,3)
plot(t,y2)
title('5*sin(2*pi*30*t)')
%滤波器的幅频相频曲线
figure(2)
[h,w] = freqz(filtb,filta,256);
%[h,f] = freqz(filtb,filta,256,Fs);
subplot(2,1,1)
plot(w/pi,20*log10(abs(h)))
%plot(f,20*log10(abs(h)))
xlabel('\times\pi')
%xlabel('Hz')
ylabel('gain(dB)')
subplot(2,1,2)
plot(w/pi,angle(h))
%plot(f,angle(h))
xlabel('\times\pi')
%xlabel('Hz')
ylabel('phase (rad)')