Theoretical Analysis of the Second-order Synchrosqueezing Transform

Ratikanta Behera (1) , Sylvain Meignen (1) , Thomas Oberlin (2)

1 CVGI - Calcul des Variations, Géométrie, Image
2 IRIT-SC - Signal et Communications

In this paper, we present a theoretical analysis of the synchrosqueezing transform adapted to multicomponent signals made of strongly frequency modulated modes, which was recently proposed in the short time Fourier transform framework [13]. Before dealing in detail with the theoretical aspect, we explain throughout numerical simulations why the hypotheses made on the modes making up the multicomponent signal must be different when one considers wavelet or STFT based synchrosqueezing. After having recalled the main results regarding the original synchrosqueezing transform applied to multicomponent signals made of modes with weak frequency modulation, we prove the same kind of results for the novel synchrosqueezing transform adapted to strongly frequency modulated modes defined in [13].

Mots clés: time-frequency analysis; synchrosqueezing transform; multicomponent signals

Domaines: Analyse numérique [math.NA]

Ratikanta Behera, Sylvain Meignen, Thomas Oberlin. Theoretical Analysis of the Second-order Synchrosqueezing Transform. Applied and Computational Harmonic Analysis, 2018, 45 (2), pp.379-404. ⟨10.1016/j.acha.2016.11.001⟩. ⟨hal-01220017v3⟩