The Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes

TL;DR

This paper develops an optimal kernel-based method for estimating the scale invariant Wigner spectrum of Gaussian locally self-similar processes, including new process classes, with performance validated through simulations.

Contribution

It introduces a minimum mean-square optimal kernel approach for SIWS estimation of Gaussian LSSPs and generalizes to new process classes with demonstrated effectiveness.

Findings

Optimal kernels minimize mean-square error in SIWS estimation.

The method effectively estimates global and local SIWS.

Simulation results confirm high accuracy of the proposed estimators.

Abstract

We study locally self-similar processes (LSSPs) in Silverman's sense. By deriving the minimum mean-square optimal kernel within Cohen's class counterpart of time-frequency representations, we obtain an optimal estimation for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of estimators is completely characterized in terms of kernels, so the optimal kernel minimizes the mean-square error of the estimation. We obtain the SIWS estimation for two cases: global and local, where in the local case, the kernel is allowed to vary with time and frequency. We also introduce two generalizations of LSSPs: the locally self-similar chrip process and the multicomponent locally self-similar process, and obtain their optimal kernels. Finally, the performance and accuracy of the estimation is studied via simulation.