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Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain

In English

Författare

Summary, in English

In stochastic time-frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the ambiguity domain, with the advantage that the mean square error optimal ambiguity kernel can be computed. For processes in discrete time, several ambiguity domain definitions have been proposed. It has previously been reported that in the Jeong-Williams ambiguity domain, in contrast to the Nutall and the Claasen-Mecklenbräucker ambiguity domain, any smoothing covariance function estimator can be represented as an ambiguity kernel function. In this paper, we show that the Jeong-Williams ambiguity domain can not be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the ambiguity domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.

Avdelning/ar

Publiceringsår

2010

Språk

Engelska

Sidor

2203-2211

Publikation/Tidskrift/Serie

Signal Processing

Volym

90

Issue

7

Dokumenttyp

Artikel i tidskrift

Förlag

Elsevier

Ämne

  • Probability Theory and Statistics

Nyckelord

  • Time-frequency analysis
  • Auto Covariance Sequence (ACVS)
  • Ambiguity domain

Status

Published

Forskningsgrupp

  • Statistical Signal Processing Group

ISBN/ISSN/Övrigt

  • ISSN: 0165-1684