Analysis of non-Gaussian processes using the Wiener model of discrete nonlinear systems

Abstract

Fundamental results developed by Wiener in the 1950's are combined with new work in the area of higher-order statistics to develop and explore a general model for nonlinear stochastic processes. The Wiener model is developed for discrete nonlin- ear systems and its orthogonality properties are analyzed to characterize its output statistics. An efficient structured procedure for computing the fc th -order statistics of the model output is formulated in both the time and frequency domains. Explicit formulas that exploit the structure of the Wiener model are given for computing the cumulants and polyspectra. A necessary condition for a discrete random process to be representable by the Wiener model is discussed. A computationally efficient pro- cedure is given for matching the model output cumulants to estimated cumulants for a given process by minimizing the squared magnitude of the error. Examples of applying this procedure to given sets of data are presented.