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

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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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Correspondence to Maria Hansson-Sandsten.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hansson-Sandsten, M. Optimal Multitaper Wigner Spectrum Estimation of a Class of Locally Stationary Processes Using Hermite Functions. EURASIP J. Adv. Signal Process. 2011, 980805 (2011) doi:10.1155/2011/980805

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Keywords

  • Information Technology
  • Stationary Process
  • Quantum Information
  • Window Length
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