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

Wei Xiong; Hualiang Li; Tüay Adali; Yi Ou Li; Vince D. Calhoun

doi:10.1109/TSP.2010.2040411

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

Wei Xiong, Hualiang Li, Tüay Adali, Yi Ou Li, Vince D. Calhoun

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Article number	5378620
Pages (from-to)	2409-2414
Number of pages	6
Journal	IEEE Transactions on Signal Processing
Volume	58
Issue number	4
DOIs	https://doi.org/10.1109/TSP.2010.2040411
State	Published - Apr 2010
Externally published	Yes

Keywords

Complex-valued signal processing
Entropy rate
Order selection

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2010.2040411

Cite this

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AU - Adali, Tüay

AU - Li, Yi Ou

AU - Calhoun, Vince D.

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AB - 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.

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

Abstract

Keywords

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