Comptes Rendus
no. 5
Fourier and the science of today / Fourier et la science d'aujourd'hui
Synchrosqueezing transforms: From low- to high-frequency modulations and perspectives
[La transformée synchrosqueezée, adaptation aux signaux fortement modulés et perspectives]
Sylvain Meignen1  ; Thomas Oberlin2 ; Duong-Hung Pham3
1 Laboratoire LJK, bâtiment IMAG, Université Grenoble Alpes, 700, avenue Centrale, Campus de Saint-Martin-d'Hères, 38401 Domaine universitaire de Saint-Martin-d'Hères, France
2 IRIT, Toulouse INP – ENSEEIHT, 2, rue Charles-Camichel, BP 7122, 31071 Toulouse cedex 7, France
3 ICube, UMR 7357, Laboratoire des sciences de l'ingènieur, de l'informatique et de l'imagerie, 300, bd Sébastien-Brant, CS 10413, 67412 Illkirch cedex, France
Comptes Rendus. Physique, Volume 20 (2019) no. 5, pp. 449-460.

Dans cet article, nous présentons le principe de la transformée synchrosqueezée (SST) développée pour améliorer, en utilisant des techniques de réallocation, la qualité des représentations linéaires temps–fréquence, comme les transformées de Fourier à court terme ou en ondelettes. Les transformées réallouées demeurent inversibles, ce qui est fondamental pour l'étude des signaux multicomposantes (MCS), i.e. la superposition de modes modulés à la fois en amplitude et en fréquence, utilisés comme modèle dans de nombreuses applications. Cependant, la SST, dans sa formulation initiale, n'est pas adaptée aux signaux composés de modes fortement modulés, et des améliorations, que nous présentons ici, ont récemment été proposées pour pallier ce défaut. Pour illustrer ces nouveaux développements, nous étudierons le cas des ondes gravitationnelles et des modes à phase oscillante. Dans un second temps, nous montrerons comment utiliser conjointement la SST et la démodulation pour améliorer la reconstruction des modes d'un MCS, et terminerons en évoquant différentes perspectives actuelles autour de la SST.

The general aim of this paper is to introduce the concept of synchrosqueezing transforms (SSTs) that was developed to sharpen linear time–frequency representations (TFRs), like the short-time Fourier or the continuous wavelet transforms, in such a way that the sharpened transforms remain invertible. This property is of paramount importance when one seeks to recover the modes of a multicomponent signal (MCS), corresponding to the superimposition of AM/FM modes, a model often used in many practical situations. After having recalled the basic principles of SST and explained why, when applied to an MCS, it works well only when the modes making up the signal are slightly modulated, we focus on how to circumvent this limitation. We then give illustrations in practical situations either associated with gravitational wave signals or modes with fast oscillating frequencies and discuss how SST can be used in conjunction with a demodulation operator, extending existing results in that matter. Finally, we list a series of different perspectives showing the interest of SST for the signal processing community.

Publié le :
DOI : 10.1016/j.crhy.2019.07.001
Keywords: Time-frequency analysis, Multicomponent signals, Reassignment techniques
Mot clés : Analyse temps-fréquence, Signaux multicomposantes, Techniques de réallocation
Sylvain Meignen 1 ; Thomas Oberlin 2 ; Duong-Hung Pham 3

1 Laboratoire LJK, bâtiment IMAG, Université Grenoble Alpes, 700, avenue Centrale, Campus de Saint-Martin-d'Hères, 38401 Domaine universitaire de Saint-Martin-d'Hères, France
2 IRIT, Toulouse INP – ENSEEIHT, 2, rue Charles-Camichel, BP 7122, 31071 Toulouse cedex 7, France
3 ICube, UMR 7357, Laboratoire des sciences de l'ingènieur, de l'informatique et de l'imagerie, 300, bd Sébastien-Brant, CS 10413, 67412 Illkirch cedex, France 
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Sylvain Meignen; Thomas Oberlin; Duong-Hung Pham. Synchrosqueezing transforms: From low- to high-frequency modulations and perspectives. Comptes Rendus. Physique, Volume 20 (2019) no. 5, pp. 449-460. doi : 10.1016/j.crhy.2019.07.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.07.001/

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