Instantaneous Frequency Band and Synchrosqueezing in Time-Frequency Analysis

Synchrosqueezing transform (SST) has been proposed to characterize frequency-modulated signals with slow varying instantaneous frequency (IF). However, it cannot generate highly concentrated TF representations (TFR) for signals with fast varying IF, and is easily contaminated by noise. In this paper, instantaneous frequency band (IFB) and its width are defined such that a new TFA method called statistic synchrosqueezing transform (Stat-SST) is proposed to characterize the fast varying IF of noisy signals in a concentrated and noise-reduced way. Firstly, we define the IFB to improve the property of IF estimator of SST and reassign TF coefficients so that the concentration of TFR can be enhanced. Then we distinguish signal from noise by using a threshold obtained by IFB width, thus the noise can be greatly removed. As a result, Stat-SST provides an energy-concentrated and noise-reduced TFR and retains the reconstruction capability. We employ both numerical simulation data and practical aero-engine data to verify that Stat-SST is superior, more concentrated, and more robust to some existing TFA methods, especially when analyzing signals with fast varying IF.