Value of cross correlation in matlab?

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?

Answer 1

[Adam Danz]

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)

Demo:

sig1 = 1./(1+exp(-5:5));
sig2 = 1./(1+exp(-6:4));

plot(sig1); 
hold on
plot(sig2);

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

[Kalasagarreddi Kottakota]

Thanks for you response. These fuctions are working for equal length of signals. But are there any function for cross-correlation of unequal signal lengths?

[Image Analyst]

Try using interp1 or spline to resample one of your signals so that it has the same number of samples as the other signal.

[Adam Danz]

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.