Polynomial time-frequency distributions and time-varying higher order spectra: Application to the analysis of multicomponent FM signals and to the treatment of multiplicative noise

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Polynomial time-frequency distributions and time-varying higher order spectra: Application to the analysis of multicomponent FM signals and to the treatment of multiplicative noise

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Title: Polynomial time-frequency distributions and time-varying higher order spectra: Application to the analysis of multicomponent FM signals and to the treatment of multiplicative noise
Author: Boashash, Boualem; Ristic, Branko
Abstract: One of the fundamental problems of time–frequency analysis that remained unsolved until recently is the time–frequency representation of signals with an arbitrary non-linear frequency variation in time. A certain type of higher-order time–frequency distributions (TFDs), referred to as polynomial Wigner-Ville distributions (PWVDs), can achieve delta function concentration in the time–frequency plane for mono-component polynomial FM signals (Boashash and O’Shea, 1994). This paper is a sequel to Boashash and O’Shea (1994) dealing with a broader class of signals and presenting an application to the treatment of multiplicative noise. The first part of the paper presents a general design procedure for PWVDs and the main properties of PWVDs. A specific class of polynomial time–frequency distributions that deals effectively with multicomponent signals is then described. In the second part of the paper we deal with random signals and introduce time-varying higher-order spectra (TV-HOS) an ensemble averaged PWVDs. TV-HOS are shown to be natural tools for analysis of non-stationary random signals, and we demonstrate this in the context of FM signals affected by multiplicative noise. Both moment and cumulant fourth-order TV-HOS, referred to as the Wigner-Ville trispectra are shown to be superior to the second-order methods for this application.
Description: This paper was one of the first papers to relate the notions of Time-Frequency Analysis and Higher Order Spectra and apply to multicomponent FM signal analysis in additive and multiplicative noise.
URI: http://hdl.handle.net/10576/10652
Date: 1998-05

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