Took, Mandic: Augmented second-order statistics of quaternion random signals


by Clive Cheong Took, Danilo P. Mandic,
Department of Electrical and Electronic Engineering, Imperial College, London SW72AZ, UK,
Signal Processing 91 (2011) 214–224.

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 pseudo covariance of such processes, the use of ı-E-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.

Keywords:
Quaternion random variables, Augmented quaternion statistics, Q-properness, Widely linear modelling, Multivariate Gaussian distribution, Quadrivariate entropy, Quadrivariate random processes, Second order circularity, Widely linear quaternion Wiener model

Source: Email by D. Mandic (d.mandicATimperial.ac.uk), 2011/01/19 0:43

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