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

TL;DR

This paper presents an efficient multitaper method for optimally estimating the scale invariant Wigner spectrum of Gaussian locally self-similar processes, utilizing Hermite functions for improved computational performance.

Contribution

It introduces a novel estimation approach using Hermite functions and the quasi Lamperti transformation, enhancing efficiency and accuracy in spectral estimation.

Findings

Optimal estimation achieved with reduced mean square error

Hermite functions effectively approximate optimal multitapers

Simulation confirms improved performance and accuracy

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.