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Circular Cross Correlation

by G. Levin

26 Apr 2004 (Updated 16 Aug 2004)

Code covered by BSD License

Circular Cross Correlation function estimate.

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Description

CXCORR Circular Cross Correlation function estimates.
CXCORR(a,b), where a and b represent samples taken over time interval T which is assumed to be a common period of two corresponding periodic signals.

a and b are supposed to be length M row vectors, either real or complex.

[x,c]=CXCORR(a,b) returns the length M-1 circular cross correlation sequence c with corresponding lags x.

The circular cross correlation is:
c(k) = sum[a(n)*conj(b(n+k))]/[norm(a)*norm(b)];
where vector b is shifted CIRCULARLY by k samples.

The function doesn't check the format of input vectors a and b!

For circular covariance between a and b look for CXCOV(a,b) in
http://www.mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectType=author&objectId=1093734

Reference:
A. V. Oppenheim, R. W. Schafer and J. R. Buck, Discrete-Time Signal Processing, Upper Saddler River, NJ : Prentice Hall, 1999.

Author: G. Levin, April 2004.

Acknowledgements

This submission has inspired the following:
Fast Circular (Periodic) Cross Correlation, Circular Statistics Toolbox (Directional Statistics)

MATLAB release

MATLAB 6.5 (R13)

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Everyone's Tags	correlation, estimation, filter analysis, filter design, statistics
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Comments and Ratings (5)
09 Jun 2004	Neil King	Excellent, this is exactly what i was looking for!!! Ive been trying to correlate optical field profiles and this is the best tool that ive found
17 Jan 2006	m g
19 Apr 2006	§õ ©_À·	try it
23 Mar 2008	Steffen B.	Very useful for my term project, thanks.
10 Sep 2009	Paul Lin	How come the mean of a and b are not subtracted before divided by norm? I'm assuming the result is a normalized norm , please corect me if I'm wrong.

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Updates
10 Jun 2004	Misspell correction
16 Aug 2004	Misspell correction. Add help.
16 Aug 2004	Misspell correction. Add help.

Tag Activity for this File
Tag	Applied By	Date/Time
filter design	G. Levin	22 Oct 2008 07:18:30
filter analysis	G. Levin	22 Oct 2008 07:18:30
correlation	G. Levin	22 Oct 2008 07:18:30
estimation	G. Levin	22 Oct 2008 07:18:30
statistics	G. Levin	22 Oct 2008 07:18:30

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