MATLAB: Cross Correlation

MATLABsignal processingstatistics

What does the function xcorr(x,y) actually do? Is it just a multiplication of Xm+n and Yn ? If so, why does the result matrix have 2N-1 elements while X & Y have N elements? How do I conclude if there is correlation among X & Y from the result? Thanks

Best Answer

xcorr computes the cross correlation sequence which is attained by shifting one sequence with respect to the other, complex conjugating it, taking the element by element product, and summing the result.

You typically want to compute the cross correlation sequence when you want to compute the "correlation" between a time series and shifted versions of another series.

For example, the following shows that y is a delayed version of x and the delay is 5 samples.

rng default;
x = randn(10,1);
y = [zeros(5,1); x];
[C,lags] = xcorr(y,x);
stem(lags,C);

Perhaps what you want is corrcoef() to compute the correlation between two random vectors?

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MATLAB: Formula for cross-correlation in matlab

It looks like that 'xcorr' does not calculate Pearson correlation coefficient directly. To get Pearson correlation coefficient, we have to remove the mean first and then call 'xcorr' which will then give Pearson correlation coefficient.

MATLAB: Covariance and correlation

Hi, In investigating correlation between two time series, you may want to use xcorr() to obtain the cross correlation sequence.

The cross correlation sequence lags one time series with respect to the other and gives the correlation at different lags. This is often a better measure for time series. For example if two time series are identical except that one arrives at a sensor a few milliseconds after another, then the correlation may be small, but is that really accurate. If you lag one with respect to the other you can see that they are perfectly correlated at a given lag.

In the following example, y is a delayed version of x (delayed by ten samples). If you just compute the correlation, it is pretty small (approx. 0.16), but if you use the cross correlation sequence, you see that y and x are perfectly correlated at lag 10 as expected.

x = randn(100,1);
y = [zeros(10,1) ; x(1:90)];
[c,lags] = xcorr(y,x,50,'coeff');
stem(lags,c); xlabel('Lag');
ylabel('Correlation Coefficient');

Best Answer

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MATLAB: Formula for cross-correlation in matlab

MATLAB: Covariance and correlation

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