脉冲响应与频率响应的关系

因为脉冲信号的频谱是全频段的，如下所示。



所以滤波器脉冲响应的傅立叶变换即为滤波其的频率响应，下图为fvtool得到的频率滤波器频率响应。



滤波器的脉冲响应如下图所示。



脉冲响应的FFT变换如下。



本例源程序如下：

clear
clc

%frequency of impluse
Impluse = zeros(1,1024);
F=linspace(0,2,1024);
Impluse(1)=1;
IMP = fft(Impluse);
IMP = abs(IMP);
figure
plot(F(1:512),IMP(1:512));
grid on

% generate filter
Fpass = 0.15;  % Passband Frequency
Fstop = 0.2;   % Stopband Frequency
Apass = 1;     % Passband Ripple (dB)
Astop = 60;    % Stopband Attenuation (dB)

h = fdesign.lowpass('fp,fst,ap,ast', Fpass, Fstop, Apass, Astop);

Hd = design(h, 'equiripple', ...
'MinOrder', 'any', ...
'StopbandShape', 'flat');
fvtool(Hd)

% plot filter's impluse response
HdImpluse = Hd.Numerator;
figure
plot(HdImpluse)
grid on

HdImp=zeros(1,1024);
HdImp(1:length(HdImpluse))=HdImpluse;
HDIMP = fft(HdImp);
HDIMP = abs(HDIMP);
figure
plot(F(1:512),20*log10(HDIMP(1:512)));
grid on