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Theoretical analysis of the second-order synchrosqueezing transform

Behera, Ratikanta and Meignen, Sylvain and Oberlin, Thomas Theoretical analysis of the second-order synchrosqueezing transform. (2018) Applied and Computational Harmonic Analysis, 45 (2). 379-404. ISSN 1063-5203

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Official URL: https://doi.org/10.1016/j.acha.2016.11.001

Abstract

We consider in this article the analysis of multicomponent signals, defined as superpositions of modulated waves also called modes. More precisely, we focus on the analysis of a variant of the second-order synchrosqueezing transform, which was introduced recently, to deal with modes containing strong frequency modulation. Before going into this analysis, we revisit the case where the modes are assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. [8], to show that the constraint on the compactness of the analysis window in the Fourier domain can be alleviated. We also explain why the hypotheses made on the modes making up the multicomponent signal must be different when one considers either wavelet or short-time Fourier transform-based synchrosqueezing. The rest of the paper is devoted to the theoretical analysis of the variant of the second order synchrosqueezing transform [16] and numerical simulations illustrate the performance of the latter.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Institut polytechnique de Grenoble (FRANCE)
French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Other partners > Université Grenoble Alpes - UGA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited On:27 Apr 2020 12:56

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