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

Harold Omer (1) , Bruno Torrésani (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 IRL CRM-CNRS - International Research Lab

A class of random non-stationary signals termed timbre×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.

Mots clés: Stationary signals; Warping; Modulation; Time-scale; Time-frequency

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Statistiques [math.ST]

Harold Omer, Bruno Torrésani. Time-frequency and time-scale analysis of deformed stationary processes, with application to non-stationary sound modeling. Applied and Computational Harmonic Analysis, 2017, 43 (1), pp.1-22. ⟨10.1016/j.acha.2015.10.002⟩. ⟨hal-01094835v2⟩