滤波器设计-巴特沃尔斯低通滤波设计 转

Fs = 1000;                                                                        %采样率
N  = 1000;                                                                        %采样点数
n  = 0:N-1;
t   = 0:1/Fs:1-1/Fs;                                                            %时间序列
Signal_Original_1 =sin(2*pi*10*t)+sin(2*pi*20*t)+sin(2*pi*30*t);
Noise_White_1    = [0.3*randn(1,500), rand(1,500)];           %前500点高斯分部白噪声，后500点均匀分布白噪声
Mix_Signal_1   = Signal_Original_1 + Noise_White_1;        %构造的混合信号

Signal_Original_2  =  [zeros(1,100), 20*ones(1,20), -2*ones(1,30), 5*ones(1,80), -5*ones(1,30), 9*ones(1,140), -4*ones(1,40), 3*ones(1,220), 12*ones(1,100), 5*ones(1,20), 25*ones(1,30), 7 *ones(1,190)];
Noise_White_2     =  0.5*randn(1,1000);                                 %高斯白噪声
Mix_Signal_2        =  Signal_Original_2 + Noise_White_2;      %构造的混合信号

%****************************************************************************************
% 
%                信号Mix_Signal_1 和 Mix_Signal_2  分别作巴特沃斯低通滤波。
%
%***************************************************************************************

%混合信号 Mix_Signal_1  巴特沃斯低通滤波
figure(1);
Wc=2*50/Fs;                                          %截止频率 50Hz
[b,a]=butter(4,Wc);
Signal_Filter=filter(b,a,Mix_Signal_1);

subplot(4,1,1);                                        %Mix_Signal_1 原始信号                
plot(Mix_Signal_1);
axis([0,1000,-4,4]);
title('原始信号 ');

subplot(4,1,2);                                        %Mix_Signal_1 低通滤波滤波后信号 
plot(Signal_Filter);
axis([0,1000,-4,4]);
title('巴特沃斯低通滤波后信号');

%混合信号 Mix_Signal_2  巴特沃斯低通滤波
Wc=2*100/Fs;                                          %截止频率 100Hz
[b,a]=butter(4,Wc);
Signal_Filter=filter(b,a,Mix_Signal_2);

subplot(4,1,3);                                        %Mix_Signal_2 原始信号                
plot(Mix_Signal_2);
axis([0,1000,-10,30]);
title('原始信号 ');

subplot(4,1,4);                                       %Mix_Signal_2 低通滤波滤波后信号 
plot(Signal_Filter);
axis([0,1000,-10,30]);
title('巴特沃斯低通滤波后信号');