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 journalArticle

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 languageEnglish (US)
Article number5378620
Pages (from-to)2409-2414
Number of pages6
JournalIEEE Transactions on Signal Processing
Volume58
Issue number4
DOIs
StatePublished - Apr 1 2010
Externally publishedYes

Keywords

  • Complex-valued signal processing
  • Entropy rate
  • Order selection

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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