jens
b31f3e7435
git-svn-id: http://moon:8086/svn/matlab/trunk@153 801c6759-fa7c-4059-a304-17956f83a07c
34 lines
1.6 KiB
Matlab
Executable File
34 lines
1.6 KiB
Matlab
Executable File
% sidex.m - Demonstration of using FFT cross-correlation to compute
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% the impulse response of a filter given its input and output.
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% This is called "FIR system identification".
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Nx = 256; % input signal length
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Nh = 100; % filter length
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Ny = Nx+Nh-1; % max output signal length
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% FFT size to accommodate cross-correlation:
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Nfft = 2^nextpow2(Nx+Ny-1); % want power of 2 for FFT
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%x = rand(1,Nx); % input signal = noise
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x = 1:Nx; % input signal = ramp
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h = [1:Nh]; % the filter
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xzp = [x,zeros(1,Nfft-Nx)]; % zero-padded input signal
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yzp = filter(h,1,xzp); % apply the filter
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X = fft(xzp); % input spectrum
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Y = fft(yzp); % output spectrum
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Rxx = conj(X) .* X; % energy spectrum of x
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Rxy = conj(X) .* Y; % cross-energy spectrum of x and y
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Hxy = Rxy ./ Rxx; % should be the freq. response
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hxy = ifft(Hxy); % should be the imp. response
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hxy(1:Nh) % print estimated impulse response
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%freqz(hxy,1,Nfft); % plot estimated frequency response
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plot(1:lge(hxy),real(hxy));
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err = norm(hxy - [h,zeros(1,Nfft-Nh)])/norm(h);
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disp(sprintf('Impulse Response Error = %0.14f%%',100*err));
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err = norm(Hxy - fft([h,zeros(1,Nfft-Nh)]))/norm(h);
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disp(sprintf('Frequency Response Error = %0.14f%%',100*err));
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