Cross Correlation

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

Answer 1

[Wayne King]

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?

[Nithin]

Hi, Thanks for your reply. I am looking to do a cross correlation between velocity and its corresponding acceleration with a delay. Or velocity with a shifted velocity. In either case, I do not know how to conclude if there exists a correlation between the two time series

[Wayne King]

By the way, by default xcorr computes the cross correlation at 2*N-1 lags. If x and y are both length 3 for example, the lags run from:

-2,-1,0,1,2. You can specify the maxlag to be something less than that. See the help.

Answer 2

[Wayne King]

velocity with a shifted velocity will definitely work with xcorr. Since acceleration is the derivative of velocity, if you have acceleration with a delay, you'll have to get the derivative of the velocity vector first to use xcorr().

[Nithin]

I have the derivative and even the delayed version of the same time series. But my question is, how can I decisively conclude if there is a correlation between the velocity and a delayed version of it? If there is correlation, what would quantify the extent of the correlation? Thanks again for your answers!

[Wayne King]

If they are the same length, then you can use the 'coeff' option and you will have a cross correlation that ranges from [-1, 1]. You can look at the lag at which the largest correlation coefficient occurs and what it's value is.