Adaptive signal processing
Random signals and systems
Nonlinear time series analysis
Nonlinear time series analysis
Statistical Digital Signal Processing and Modeling
Statistical Digital Signal Processing and Modeling
A non-parametric test for detecting the complex-valued nature of time series
International Journal of Knowledge-based and Intelligent Engineering Systems - Advanced Intelligent Techniques in Engineering Applications
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
ARMA Prediction of Widely Linear Systems by Using the Innovations Algorithm
IEEE Transactions on Signal Processing - Part II
Exact expectation analysis of the LMS adaptive filter
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Mean-square performance of a convex combination of two adaptive filters
IEEE Transactions on Signal Processing
Second-order analysis of improper complex random vectors and processes
IEEE Transactions on Signal Processing
Widely linear estimation with complex data
IEEE Transactions on Signal Processing
Proper complex random processes with applications to information theory
IEEE Transactions on Information Theory
Adaptive mixture methods based on Bregman divergences
Digital Signal Processing
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A real-time approach for the identification of second-order noncircularity (improperness) of complex valued signals is introduced. This is achieved based on a convex combination of a standard and widely linear complex adaptive filter, trained by the corresponding complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms. By providing a rigorous account of widely linear autoregressive modelling the analysis shows that the monitoring of the evolution of the adaptive convex mixing parameter within this structure makes it possible to both detect and track the complex improperness in real time, unlike current methods which are block based and static. The existence and uniqueness of the solution are illustrated through the analysis of the convergence of the convex mixing parameter. The analysis is supported by simulations on representative datasets, for a range of both proper and improper inputs.