On entropy rate for the complex domain and its application to i.i.d. sampling

Authors:
Wei Xiong;Hualiang Li;Tülay Adali;Yi-Ou Li;Vince D. Calhoun
Affiliations:
Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD;Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD;Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD;Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD;Department of Electrical and Computer Engineering, University of New Mexico, and MIND Research Network, Albuquerque, NM
Venue:
IEEE Transactions on Signal Processing
Year:
2010

Citing 8
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Abstract

We derive the entropy rate formula for a complex Gaussian random process by using a widely linear model. The resulting expression is general and applicable to both circular and noncircular Gaussian processes, since any second-order stationary process can be modeled as the output of a widely linear system driven by a circular white noise. Furthermore, we demonstrate application of the derived formula to an order selection problem. We extend a scheme for independent and identically distributed (i.i.d.) sampling to the complex domain to improve the estimation performance of information-theoretic criteria when samples are correlated. We show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging (fMRI) data that are inherently complex valued.