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

H Omer (1) , B Torrésani (1)

1 I2M - Institut de Mathématiques de Marseille

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

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

H Omer, B Torrésani. Time-frequency and time-scale analysis of deformed stationary processes, with application to non-stationary sound modeling. 2014. ⟨hal-01094835v1⟩