The Fourier-based Synchrosqueezing Transform

Thomas Oberlin (1) , Sylvain Meignen (1) , Valérie Perrier (1)

1 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

The short-time Fourier transform (STFT) and continuous wavelet transform (CWT) are intensively used to analyze and process multicomponent signals, ie superpositions of mod- ulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relations, inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the continuous wavelet transform, it provides a sharp, con- centrated representation, while remaining invertible. This technique received a renewed interest with the recent publi- cation of an approximation result, which provides guarantees for the decomposition of a multicomponent signal. This paper adapts the formulation of the synchrosqueezing to the STFT, and states a similar theoretical result. The emphasis is put on the differences with the CWT-based synchrosqueezing, and all the content is illustrated through numerical experiments.

Mots clés: multicomponent signals; short-time Fourier transform; ridge analysis; synchrosqueezing; reassignment

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Thomas Oberlin, Sylvain Meignen, Valérie Perrier. The Fourier-based Synchrosqueezing Transform. 2013. ⟨hal-00916088⟩