Time-frequency and time-scale analysis of deformed stationary processes, with application to non-stationary sound modeling

TL;DR

This paper introduces methods for analyzing non-stationary signals, specifically modulation and time warping, using time-frequency and time-scale representations, with applications to sound modeling.

Contribution

It develops estimation algorithms for non-linear transformations of stationary signals, enabling simultaneous estimation of transformations and power spectra.

Findings

Algorithms effectively estimate modulation and warping parameters

Validated on synthetic signals and real car engine sounds

Approach improves non-stationary sound modeling accuracy

Abstract

A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be approximated by translations in an appropriate representation domain. In such situations, approximate maximum likelihood estimation techniques can be de-rived, which yield simultaneous estimation of the transformation and the power spectrum of the underlying stationary signal. This paper focuses on the case of modulation and time warping of station-ary signals, and proposes and studies estimation algorithms (based on time-frequency and time-scale representations respectively) for these quantities of interest. The proposed approach is validated on numerical simulations on synthetic signals, and examples on real life car engine sounds.