complex correlations coefficients - how to interpret?

I've got two complex signals. Now I am searching for a correlation. The Matlab-function corrcoef gives me a complex correlation coefficient (cc).

Interpreting it as usual suggests, that the abs of the cc means the characteristics of correlation. The phase must be the phase shift between the signals.

Unfortunately, I've nowhere found a documentation about complex correlation coefficients. Maybe you can give me a hint, where I can find more information.

Thank you very much for your time.

[Sascha]

Considering, that nobody can answer this question, I have to review the sense of complex correlation coefficients and their calculation. I am now considering to treat the real and imaginary part separately.

Please let me know if somebody knows something about this issue.

[Kimansuper]

hi Sascha, It's been a while since you posted this matter. To simply answer your question, take the absolute value of the complex output of corrcoef (let's call it rho_c) to find the correlation value. Moreover, the phase of the rho_c is important when you when to estimates one complex signal from one other. For more hints, please have alook at the following book: "Statistical Signal Processing of Complex-Valued Data The Theory of Improper and Noncircular Signals". PETER J. SCHREIER and LOUIS L. SCHARF

Answer 1

[Aleksandra Cupial]

Also (for other people looking up this question), work of P. Kundu might be interesting: he defines correlation coefficient where its magnitude describes the strength of the linear relationship between the magnitude of the vectors, and phase angle describes the average direction difference between both vector time series;

Kundu, P. K. 1975. Ekman veering observed near the ocean bottom. J. Phys. Oceanogr. 6, 238-242.