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%---------------------------------------------------------------------------- 
% exa031001_fftfilt.m, for example 3.11.1 
% to test fftfilt.m,and to finish the convolution of a long sequence with 
%                       a short sequence by DFT. 
%---------------------------------------------------------------------------- 
clear; 
 
% 用叠接相加法,计算滤波器系数h和输入信号x的卷积 
% 其中h为10阶hanning窗,x是带有高斯白噪的正弦信号 
 
h=fir1(10,0.3,hanning(11));% h: a short sequence ; h is the impulse response 
N=500;p=0.05;f=1/16;       %                          of a low-pass filter. 
u=randn(1,N)*sqrt(p);      % u:white noise 
s=sin(2*pi*f*[0:N-1]);     % s:sine signal 
x=u(1:N)+s;                % x: a long sequence; 
y=fftfilt(h,x);            % y=x*h 
subplot(211) 
plot(x); 
subplot(212) 
plot(y);