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I am trying to calculate autocorrelation using fft and xcorr and plot the grafhic with both cases.
autocorr_a=xcorr(signal_1,signal_1);
N1=length(signal_1);
autocorr_b=ifft( fft(signal_1,N1) .* conj(fft(signal_1,N1)));
x1=[0:(2*length(signal_1)-2)]'/(2*length(signal_1)-1);
plot(x1, autocorr_a, x1, autocorr_b)
What is wrong?
Matlabs xcorr() command performs linear correlation, whereas the FFT method you employ performs circular correlation, so there is time-aliasing in the same way as with frequency domain convolution.
You can simulate linear convolution in the frequency domain by sufficiently zero-padding your signal with N-1 zeros, where N is the length of your signal vector, before performing the FFT.
