Synchrosqueezing transform meets α-stable distribution: An adaptive fractional lower-order SST for instantaneous frequency estimation and non-stationary signal recovery

Most of the noises in practice are non-Gaussian and presented as impulsive phenomena. Impulsive noise brings enormous difficulties for signal processing, especially for multicomponent non-stationary signal representation and separation. The synchrosqueezing transform (SST) is a time-frequency (TF) analysis method with high energy concentration and inverse transform. Although SST and its variants have been used for instantaneous frequency estimation and modes recovery in many applications, they are unable to represent the signals clearly under impulsive noise. In this paper, we model the impulsive noise with the α-stable distribution, which satisfies the generalized central limit theorem. Based on the short-time Fourier transform (STFT), we proposed the fractional lower-order SST with adaptive order and adaptive window for multicomponent signal separation with single-channel observation, called the adaptive window and fractional lower-order SST (AWO-SST). Moreover, we consider the 2nd-order phase transformation for AWO-SST and provide a component recovery method under adaptive parameters. The proposed method can be easily extended to the cases of the continuous wavelet transform, the S-transform, and other linear TF analysis methods. The experimental results demonstrate that the proposed methods have the ability to suppress the α-stable distribution noise effectively, and are capable of recovering the component signal accurately.