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

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?

Answer 1

[the cyclist]

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.

[Adib Yusof]

Thank you @the cyclist for the insight. Did you actually mean

a = repmat(a,1,5);
b = repmat(b,1,5);

to get horizontally extended signal? Thanks!

[the cyclist]

Yes I did.