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git-svn-id: http://moon:8086/svn/matlab/trunk@153 801c6759-fa7c-4059-a304-17956f83a07c
2021-03-22 20:28:22 +00:00
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+% sidex.m - Demonstration of using FFT cross-correlation to compute
+% the impulse response of a filter given its input and output.
+% This is called "FIR system identification".
+
+Nx = 256;                                   % input signal length
+Nh = 100;                                  % filter length
+Ny = Nx+Nh-1;                              % max output signal length
+
+% FFT size to accommodate cross-correlation:
+Nfft = 2^nextpow2(Nx+Ny-1);                % want power of 2 for FFT
+
+%x = rand(1,Nx);                            % input signal = noise
+x = 1:Nx; 	                           % input signal = ramp
+h = [1:Nh]; 	                           % the filter
+xzp = [x,zeros(1,Nfft-Nx)];                % zero-padded input signal
+yzp = filter(h,1,xzp);                     % apply the filter
+X = fft(xzp);                              % input spectrum
+Y = fft(yzp);                              % output spectrum
+Rxx = conj(X) .* X;                        % energy spectrum of x
+Rxy = conj(X) .* Y;                        % cross-energy spectrum of x and y
+Hxy = Rxy ./ Rxx;                          % should be the freq. response
+hxy = ifft(Hxy);                           % should be the imp. response
+
+hxy(1:Nh) 	                           % print estimated impulse response
+%freqz(hxy,1,Nfft);                        % plot estimated frequency response
+plot(1:lge(hxy),real(hxy));
+
+err = norm(hxy - [h,zeros(1,Nfft-Nh)])/norm(h);
+disp(sprintf('Impulse Response Error = %0.14f%%',100*err));
+
+err = norm(Hxy - fft([h,zeros(1,Nfft-Nh)]))/norm(h);
+disp(sprintf('Frequency Response Error = %0.14f%%',100*err));
+