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

Sandsten, Maria LU and Wahlberg, Patrik LU (2007) In IEEE Transactions on Signal Processing 55(1). p.73-84
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... (More)
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 (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Signal Processing
volume
55
issue
1
pages
73 - 84
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000243281200008
  • scopus:33947368617
ISSN
1053-587X
DOI
10.1109/TSP.2006.882076
language
English
LU publication?
yes
id
b799e99c-7ed1-4631-a805-db7a36aa7931 (old id 627350)
date added to LUP
2007-11-29 14:01:43
date last changed
2017-10-29 04:09:17
@article{b799e99c-7ed1-4631-a805-db7a36aa7931,
  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},
  author       = {Sandsten, Maria and Wahlberg, Patrik},
  issn         = {1053-587X},
  language     = {eng},
  number       = {1},
  pages        = {73--84},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Kernels and multiple windows for estimation of the Wigner-Ville spectrum of Gaussian locally stationary processes},
  url          = {http://dx.doi.org/10.1109/TSP.2006.882076},
  volume       = {55},
  year         = {2007},
}