Open Access

Optimal Multitaper Wigner Spectrum Estimation of a Class of Locally Stationary Processes Using Hermite Functions

EURASIP Journal on Advances in Signal Processing20102011:980805

https://doi.org/10.1155/2011/980805

Received: 24 June 2010

Accepted: 3 December 2010

Published: 15 December 2010

Abstract

This paper investigates the time-discrete multitapers that give a mean square error optimal Wigner spectrum estimate for a class of locally stationary processes (LSPs). The accuracy in the estimation of the time-variable Wigner spectrum of the LSP is evaluated and compared with other frequently used methods. The optimal multitapers are also approximated by Hermite functions, which is computationally more efficient, and the errors introduced by this approximation are studied. Additionally, the number of windows included in a multitaper spectrum estimate is often crucial and an investigation of the error caused by limiting this number is made. Finally, the same optimal set of weights can be stored and utilized for different window lengths. As a result, the optimal multitapers are shown to be well approximated by Hermite functions, and a limited number of windows can be used for a mean square error optimal spectrogram estimate.

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Authors’ Affiliations

(1)
Mathematical Statistics, Centre for Mathematical Sciences, Lund University

Copyright

© Maria Hansson-Sandsten. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.