Kernels and multiple windows for estimation of the Wigner-Ville spectrum of Gaussian locally stationary processes

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Abstract

This paper treats estimation of the Wigner-Ville spectrum (WVS) of Gaussian continuous-time stochastic processes using Cohen's class of time-frequency representations of random signals. We study the minimum mean square error estimation kernel for locally stationary processes in Silverman's sense, and two modifications where we first allow chirp multiplication and then allow nonnegative linear combinations of covariances of the first kind. We also treat the equivalent multitaper estimation formulation and the associated problem of eigenvalue-eigenfunction decomposition of a certain Hermitian function. For a certain family of locally stationary processes which parametrizes the transition from stationarity to nonstationarity, the optimal windows are approximately dilated Hermite functions. We determine the optimal coefficients and the dilation factor for these functions as a function of the process family parameter

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Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics
Original languageEnglish
Pages (from-to)73-84
JournalIEEE Transactions on Signal Processing
Volume55
Issue number1
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Statistics (011015003), Department of Electroscience (011041000)