Synthesis-based time-scale transforms for non-stationary signals

TL;DR

This paper introduces a synthesis-based approach for modeling non-stationary signals using a novel timescale representation, enabling accurate estimation of time warping and spectral properties even with rapid variations.

Contribution

It proposes a direct modeling method of timescale representations for non-stationary signals, along with an iterative EM-based algorithm for parameter estimation, outperforming previous methods in fast-changing scenarios.

Findings

JEFAS-S accurately estimates time warping and power spectrum.

The approach yields extremely sharp timescale representations.

It outperforms previous methods like JEFAS and synchrosqueezing in fast variations.

Abstract

This paper deals with the modeling of non-stationary signals, from the point of view of signal synthesis. A class of random, non-stationary signals, generated by synthesis from a random timescale representation, is introduced and studied. Non-stationarity is implemented in the timescale representation through a prior distribution which models the action of time warping on a stationary signal. A main originality of the approach is that models directly a timescale representation from which signals can be synthesized, instead of post-processing a pre-computed timescale transform. A maximum a posteriori estimator is proposed for the time warping parameters and the power spectrum of an underlying stationary signal, together with an iterative algorithm, called JEFAS-S, for the estimation, based upon the Expectation Maximization approach. Numerical results show the ability of JEFAS-S to estimate accurately time warping and power spectrum. This is in particular true when time warping involves fast variations, where a similar approach called JEFAS, proposed earlier, fails. In addition, as a by-product, the approach is able to yield extremely sharp timescale representations, also in the case of fast varying non-stationarity, where standard approaches such as synchrosqueezing fail.