Theoretical Analysis of the Second-order Synchrosqueezing Transform

International audienceIn 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]