Optimal Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes Using Hermite Functions

Yasaman Maleki ()
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Yasaman Maleki: Alzahra University

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 202-215

Abstract: Abstract This paper investigates the mean square error optimal estimation of scale invariant Wigner spectrum for the class of Gaussian locally self-similar processes, by the multitaper method. In this method, the spectrum is estimated as a weighted sum of scale invariant windowed spectrograms. Moreover, it is shown that the optimal multitapers are approximated by the quasi Lamperti transformation of Hermite functions, which is computationally more efficient. Finally, the performance and accuracy of the estimation is studied via simulation.

Keywords: Locally self-similar processes; Scale invariant Wigner spectrum; Multitaper method; Hermite functions; Time–frequency analysis; 60G18; 60G99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-017-0801-1

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