Value of cross correlation in matlab?

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The cross correlation function xcorr in matlab provides the lag between two signals. But, Is there any matlab function that calculates the cross correlation between 2 signals and outputs a sigle value i.e < =1?

Accepted Answer

Adam Danz
Adam Danz on 6 Jan 2023
Edited: Adam Danz on 10 Jan 2023
You could compute the cross correlation at 0 lag using r = xcorr(___,scaleopt) where scaleopt can be set to a normalization option.
If you're looking for the cross correlation coefficient, use R = corrcoef(A,B)
sig1 = 1./(1+exp(-5:5));
sig2 = 1./(1+exp(-6:4));
hold on
rm = corrcoef(sig1, sig2); % Column vectors
r2 = rm(2)
r2 = 0.9785
r1 = xcorr(sig1, sig2, 0)
r1 = 4.9234
r1norm = xcorr(sig1, sig2, 0, 'normalized')
r1norm = 0.9885
The difference is that corrcoef subtracts the mean from each vector and then normalizes the vectors to be unit vectors whereas xcorr with 'normalized' only normalizes but does not subtract the mean.
r1centered = xcorr(sig1-mean(sig1), sig2-mean(sig2), 0, 'normalized')
r1centered = 0.9785
Adam Danz
Adam Danz on 7 Jan 2023
Edited: Adam Danz on 10 Jan 2023
The only xcorr option that supports vectors of unequal length is xcorr(sig1, sig2, 0,'none') where 'none' is the default scale option so it's the same as xcorr(sig1, sig2, 0). But if you'd like to include normalization, either follow Image Analyst's advice above (interpolate the shorter vector) or trim the longer vector. Those are two very different comparisons. Interpolation resamples one of the vectors to match the length of the other vector. It's like stretching or compressing. Trimming assumes that the two signals have the same sampling interval but more data was collected in one of the signals.

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