Synchroextracting transform: the theory analysis and comparisons with the synchrosqueezing transform

Abstract In this paper, we consider the theoretical analysis and new view of a time-frequency analysis method termed synchroextracting transform (SET), which is inspired by the Fourier-based synchrosqueezing transform (FSST) and the ideal time-frequency analysis theory. We first review the corresponding definitions of the FSST and SET. Then, we provide the theoretical analysis of the SET and study some properties with mathematical proofs. We show that the SET mainly benefits from the synchroextracting operator (SEO) that can only retain the TF information most related to time-varying features of the signal. We also give a new view that SEO is equivalent to the fixed frequencies of the frequency estimation operator of the FSST. Based on the SEO, SET greatly improves the concentration of the time-frequency representation and perfectly localizes the time-frequency features of chirp signals. Finally, numerical simulations are employed to illustrate the performance comparisons of the SET and FSST.