Elements of information theory
Elements of information theory
Random signals and systems
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Audio Signal Processing for Next-Generation Multimedia Communication Systems
Audio Signal Processing for Next-Generation Multimedia Communication Systems
Quaternion involutions and anti-involutions
Computers & Mathematics with Applications
The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Properness and widely linear processing of quaternion random vectors
IEEE Transactions on Information Theory
A quaternion widely linear adaptive filter
IEEE Transactions on Signal Processing
ARMA Prediction of Widely Linear Systems by Using the Innovations Algorithm
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
Widely linear estimation with complex data
IEEE Transactions on Signal Processing
Second-order complex random vectors and normal distributions
IEEE Transactions on Signal Processing
Quaternion-MUSIC for vector-sensor array processing
IEEE Transactions on Signal Processing
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
Proper complex random processes with applications to information theory
IEEE Transactions on Information Theory
The multivariate complex normal distribution-a generalization
IEEE Transactions on Information Theory
A comparison between HMLP and HRBF for attitude control
IEEE Transactions on Neural Networks
A class of quaternion valued affine projection algorithms
Signal Processing
Prediction of wide-sense stationary quaternion random signals
Signal Processing
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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.