A fourth-order stationarity and ergodicity conditions for harmonic processes

Authors:
D. Blanco;D.P. Ruiz;E. Alameda-Hernandez;M.C. Carrion
Affiliations:
Sch. of Eng., Univ. of Edinburgh, UK;-;-;-
Venue:
IEEE Transactions on Signal Processing
Year:
2004

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Convergence analysis of a class of Hyvärinen-Oja's ICA learning algorithms with constant learning rates

IEEE Transactions on Signal Processing

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Abstract

This paper considers the problem of estimating the fourth-order cumulant sequence of a harmonic process. Both stationarity and ergodicity conditions for this kind of signal are derived through the imposition of restrictions to the frequencies and amplitudes that define the signals. Statistical properties for the mean value and the variance of the sample mean estimator are deduced as well. These conditions are applied to cubic-phase coupling detection, stressing the study of nonergodic signals and possible strategies to study them. Numerical examples to illustrate these conditions for cubic phase coupling detection and separation of mixed signals using independent component analysis (ICA) methods are also showed in this paper.