Journal of Theoretical Probability

, Volume 32, Issue 1, pp 202–215 | Cite as

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

  • Yasaman MalekiEmail author


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.


Locally self-similar processes Scale invariant Wigner spectrum Multitaper method Hermite functions Time–frequency analysis 

Mathematics Subject Classification (2010)

60G18 60G99 


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Alzahra UniversityTehranIslamic Republic of Iran

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