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Second-Order Horizontal Synchrosqueezing of the S-transform: a Specific Wavelet Case Study

We address the problem of computing efficient time-frequency and time-scale representations of non stationary multicomponent signals. Recently, a new time-reassigned synchrosqueezing method designed for the short-time Fourier transform (STFT) was introduced to improve the energy concentration of impulsive or strongly modulated signals. Following this idea, we now propose to extend this approach to the Stockwell transform (S-transform) that is related to the Morlet wavelet transform and which provides time-frequency representations with a frequency-dependent resolution. In this study, we derive an enhanced second-order group delay estimator designed for the S-transform to deal with strongly amplitude- and frequency-modulated signals. Hence, this estimator is used to obtain a novel horizontal synchrosqueezing transform that is evaluated in numerical experiments involving multicomponent non-stationary signals.