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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dc.contributor.author Boashash, Boualem
dc.contributor.author Ristic, Branko
dc.date.accessioned 2011-04-12T10:20:51Z
dc.date.available 2011-04-12T10:20:51Z
dc.date.issued 1998-05
dc.identifier.citation Signal Processing, Volume 67, Issue 1, 29 May 1998, Pages 1-23 en_US
dc.identifier.issn 0165-1684
dc.identifier.uri http://hdl.handle.net/10576/10652
dc.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. en_US
dc.description.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. en_US
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject Non-stationary signals en_US
dc.subject Time-varying signals en_US
dc.subject Instantaneous frequency en_US
dc.subject Multiplicative noise en_US
dc.subject Trispectrum en_US
dc.subject Wigner-Ville distribution en_US
dc.subject Higher-order spectra en_US
dc.subject Time-frequency analysis en_US
dc.subject Time Frequency Signal Processing en_US
dc.subject Time Frequency Distributions en_US
dc.subject Quadratic Time-Frequency distributions en_US
dc.subject Bilinear Time Frequency Distributions en_US
dc.subject Multicomponent signals en_US
dc.subject FM en_US
dc.subject Frequency Modulation en_US
dc.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 en_US
dc.type Article en_US

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