Theoretical analysis and comparison of transient-extracting transform and time-reassigned synchrosqueezing transform

Transient-extracting transform (TET) and time-reassigned synchrosqueezing transform (TSST) developed under the framework of short-time Fourier transform (STFT) can effectively enhance the time–frequency (TF) resolution of nonstationary signal composed of multicomponent with impulse-like components. Nevertheless, the TET and TSST methods lack relevant theoretical support to ensure their practical application. In this paper, we supplement the theoretical analysis of these two methods and provide a new view to compare them. We first review the original definitions of TET and TSST proposed in the previous literatures. Then, we demonstrate the performance and properties of TSST and TET in detail, e.g., group delay (GD) approximation error, reconstruction error and boundary analysis, extraction principle of TET, and property derivation. Finally, the performance of TET and TSST is further compared in the analysis of the numerical and real signals. Through complete theoretical and property analysis, the application of TET and TSST in reality can be largely enhanced.