Kernels and Multiple Windows for Estimation of the Wigner-Ville Spectrum of Gaussian Locally Stationary Processes

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...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2007-01, Vol.55 (1), p.73-84
Main Authors: Wahlberg, P., Hansson, M.
Format: Article
Language:English
Subjects:
Applied sciences
Chirp
Convolution
Councils
Estimation error
Exact sciences and technology
Information, signal and communications theory
Kernel
Locally stationary circular symmetric processes
Matematik
Mathematics
Mean square error methods
multitaper spectral estimation
Natural Sciences
Naturvetenskap
optimal estimation
Probability Theory and Statistics
Sannolikhetsteori och statistik
Signal and communications theory
Signal processing
Signal representation. Spectral analysis
Signal, noise
Spectrogram
Stochastic processes
Telecommunications and information theory
Time frequency analysis
Vågor och signaler
Waves and Signals
Wigner-Ville spectrum (WVS)
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Summary: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
ISSN:1053-587X
1941-0476
1941-0476
DOI:10.1109/TSP.2006.882076