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The synchrosqueezing transform, a kind of reassignment method, aims tosharpen the time-frequency representation and to separate the components of amulticomponent non-stationary signal. In this paper, we consider the short-timeFourier transform (STFT) with a time-varying parameter, called the adaptiveSTFT. Based on the local approximation of linear frequency modulation mode, weanalyze the well-separated condition of non-stationary multicomponent signalsusing the adaptive STFT with the Gaussian window function. We propose theSTFT-based synchrosqueezing transform (FSST) with a time-varying parameter,named the adaptive FSST, to enhance the time-frequency concentration andresolution of a multicomponent signal, and to separate its components moreaccurately. In addition, we also propose the 2nd-order adaptive FSST to furtherimprove the adaptive FSST for the non-stationary signals with fast-varyingfrequencies. Furthermore, we present a localized optimization algorithm basedon our well-separated condition to estimate the time-varying parameteradaptively and automatically. Simulation results on synthetic signals and thebat echolocation signal are provided to demonstrate the effectiveness androbustness of the proposed method.

Adaptive Short-time Fourier Transform and Synchrosqueezing Transform for Non-stationary Signal Separation