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# Cross correlation negative lag time

Asked by Sarah on 21 Sep 2012

Hi everybody, I am cross correlating two signals and plotting the lag times as delays in a histogram to see what the predominant delay is. I am getting a very prominant delag at lag time 0 to -1 hrs and am just wondering what this means in terms of which station is the causative one. By this I mean, which signal is seen first and whis is a result? Thank you for any help

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Answer by Wayne King on 21 Sep 2012
Edited by Wayne King on 21 Sep 2012

If you look at the help for xcorr(), you'll see how the inputs are lagged with respect to each other. If the A input is delayed by 4 samples with respect to B and you use:

 [xc,lags] = xcorr(A,B,...)

You'll get the maximum at the positive lag 4.

However, if you enter

[xc,lags] = xcorr(B,A,...)


you'll get the maximum at negative lag 4.

For example:

    B = randn(40,1);
% A is a delayed version of B, delayed by 4 samples
A = [zeros(4,1) ; B];
[xc,lags] = xcorr(A,B,20);
stem(lags,xc)  % delay is positive
% now reverse order of inputs
[xc,lags] = xcorr(B,A,20);
figure;
stem(lags,xc) %delay is negative

In both cases, the delay is correctly indicated as 4.

Sarah on 21 Sep 2012

Thank you for that it clears things up quite a bit. So whatever parameter is first is the driving parameter, and is seen first if the two signals are plotted on top of one another?

Wayne King on 21 Sep 2012

If you want a signal which is delayed in time relative to another to appear as a positive lag in the cross correlation, then enter that input first.

If you have a model where a signal Y is a delayed version of X, so that

Y(n) = X(n-\tau)


for some positive lag \tau, then if that is what you mean by X is driving Y, then entering

[xc,lags] = xcorr(Y,X);


gives you the maximum at lag \tau (the positive lag \tau)