Augmented second-order statistics of quaternion random signals

  • Authors:
  • Clive Cheong Took;Danilo P. Mandic

  • Affiliations:
  • Department of Electrical and Electronic Engineering, Imperial College, London SW7 2AZ, UK;Department of Electrical and Electronic Engineering, Imperial College, London SW7 2AZ, UK

  • Venue:
  • Signal Processing
  • Year:
  • 2011

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Abstract

Second order statistics of quaternion random variables and signals are revisited in order to exploit the complete second order statistical information available. The conditions for Q@?proper (second order circular) random processes are presented, and to cater for the non-vanishing pseudocovariance of such processes, the use of i@?j@?@k@?covariances is investigated. Next, the augmented statistics and the corresponding widely linear model are introduced, and a generic multivariate Gaussian distribution is subsequently derived for both Q@?proper and Q@?improper processes. The maximum entropy bound and an extension of mutual information to multivariate processes are derived in order to provide a complete description of joint information theoretic properties of general quaternion valued processes. A comparative analysis with the corresponding second order statistics of quadrivariate real valued processes supports the approach.