calculating auto-correlation function of a matrix

2016 7 5
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更新时间：2016 7 7
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Hi, How can I calculate autocorrelation of a complex matrix ? (applied on the first dimension) As far as I know xcorr() is only for vectors.
Thanks

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Honglei Chen
Honglei Chen 2016-7-6

0 个投票

Do you mean you want to compute autocorrelation for each column? If so, you can always use a for loop to do that, e.g.,
x = ones(10,2);
r = zeros(2*size(x,1)-1,size(x,2);
for m = 1:size(x,2)
r(:,m) = xcorr(x(:,m));
end
Or if you don't mind dealing with cell arrays, you can always do
x = ones(10,2);
r = arrayfun(@(n)xcorr(x(:,n),1:size(x,2),'UniformOutput',false);

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mosa mm
mosa mm 2016-7-6
编辑：mosa mm 2016-7-6
Thanks Honglei for your answer. My matrix is: 17 x 300 , after autocorrelation I should have an output of 1 x 300. Because the matrix is complex, I am guessing it must be through conjugation and sum. But I don't know how to do it.
Can you help?
Thanks
Honglei Chen
Honglei Chen 2016-7-7
It's not obvious to me what operation you want to do. There are many ways to output a 1x300 vector form a 17x300 matrix. Could you clarify how your correlation is defined?
mosa mm
mosa mm 2016-7-7
编辑：mosa mm 2016-7-7
Dear Honglei, the attached photo is the way that I should implement autocorrelation. So there are complex number multiplication (complex conjugate) and a sum. The output of this operation must give a (1 x 300) matrix in my case. Thanks
mosa mm
mosa mm 2016-7-7
the short version of the above formula:
Honglei Chen
Honglei Chen 2016-7-7
Based on that information, if I treat each column as a signal, I can have a 33x300 matrix, not a 1x300 matrix, unless we are talking about a specific time lag.

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Image Analyst
Image Analyst 2016-7-7

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There is an xcorr2() and normxcorr2() that can handle 2-D matrices like a 17 x 300 matrix. Not sure about complex numbers though - I've never tried it with those, just with real numbers. For what it's worth, I've attached a demo.

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