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

A class of random non-stationary signals termed timbre×dynamics is introduced and studied. These signals are obtained by non-linear transformations of stationary 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 derived, 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 stationary signals, and proposes and studies estimation algorithms (based on timefrequency 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.