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

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Author

Summary, in English

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

Publishing year

2007

Language

English

Pages

73-84

Publication/Series

IEEE Transactions on Signal Processing

Volume

55

Issue

1

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Probability Theory and Statistics

Status

Published

Research group

  • Statistical Signal Processing Group

ISBN/ISSN/Other

  • ISSN: 1053-587X