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Why is xcorr getting this very simple case "wrong"?

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Mitch Hezel
Mitch Hezel on 11 Feb 2021
Answered: the cyclist on 12 Feb 2021
I'm sure it's just me, but I have
a = [1 2 3 4 5 4 3 2 1];
b = [0 1 2 3 4 5 4 3 2];
[c,lags] = xcorr(detrend(a,0), detrend(b,0), 'normalized');
Then i try
lags(c == max(c))
%ans 0
Why doesn't xcorr believe the lag should be 1 sample?

Accepted Answer

the cyclist
the cyclist on 12 Feb 2021
I didn't figure this out with certainty, but if you take a look at the "More About" section of the documentation for xcorr, it mentions that xcorr can only approximate the true cross-correlation if an infinite-length signal, due to the finite length of the input vector. So, I think what is happening is that the end effects are overwhelming the "true" lag result.
I confirmed this by using
a = repmat(a,5,1);
b = repmat(b,5,1);
to get more extended signal, and you do see the lag=-1 dominate.
FYI, using
stem(lags,c)
is a good way to visualize the results.

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