signal processing - Cross-correlation in matlab without using the inbuilt function?

Question

can someone tell how to do the cross-correlation of two speech signals (each of 40,000 samples) in MATLAB without using the built-in function xcorr and the correlation coefficient?

Thanks in advance.

Answer 1

You can do cross-correlations using fft. The cross-correlation of two vectors is simply the product of their respective Fourier transforms, with one of the transforms conjugated.

Example:

a=rand(5,1);
b=rand(5,1);
corrLength=length(a)+length(b)-1;

c=fftshift(ifft(fft(a,corrLength).*conj(fft(b,corrLength))));

Compare results:

c =

    0.3311
    0.5992
    1.1320
    1.5853
    1.5848
    1.1745
    0.8500
    0.4727
    0.0915

>> xcorr(a,b)

ans =

    0.3311
    0.5992
    1.1320
    1.5853
    1.5848
    1.1745
    0.8500
    0.4727
    0.0915