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Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2011, Article ID 980805, 15 pages doi:10.1155/2011/980805 Research Article Optimal Multitaper Wigner Spectrum Estimation of a Class of Locally Stationary Processes Using Hermite Functions Maria Hansson-Sandsten (EURASIP Member) Mathematical Statistics, Centre for Mathematical Sciences, Lund University, P.O. Box 118, 221 00 Lund, Sweden Correspondence should be addressed to Maria Hansson-Sandsten, sandsten@maths.lth.se Received 24 June 2010; Revised 27 October 2010; Accepted 3 December 2010 Academic Editor: Haldun emduh Ozaktas Copyright © 2011 Maria Hansson-Sandsten. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and. | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2011 Article ID 980805 15 pages doi 10.1155 2011 980805 Research Article Optimal Multitaper Wigner Spectrum Estimation of a Class of Locally Stationary Processes Using Hermite Functions Maria Hansson-Sandsten EURASIP Member Mathematical Statistics Centre for Mathematical Sciences Lund University P.O. Box 118 221 00 Lund Sweden Correspondence should be addressed to Maria Hansson-Sandsten sandsten@maths.lth.se Received 24 June 2010 Revised 27 October 2010 Accepted 3 December 2010 Academic Editor Haldun emduh Ozaktas Copyright 2011 Maria Hansson-Sandsten. 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. 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. 1. Introduction A locally stationary process LSP has a covariance function which is a multiplication of a covariance function of a stationary process and a time-variable function 1 . The process is .
