Local maximum synchrosqueezing adaptive transformation for cross-instantaneous frequencies analysis

Abstract To overcome the shortcomings of existing time-frequency (TF) analysis (TFA) methods in analyzing signals containing cross-instantaneous frequencies (IFs), this paper proposes an adaptive TFA technique combined with image processing methods based on local maximum synchrosqueezing transform (SST). The core idea of the proposed algorithm is to localize the filtering of signals containing several different IF components using kernel functions containing several different directions, respectively, to achieve energy separation at the crossing frequencies. In turn, the local maximum SST is used to rearrange the TF energy to the true IF ridges of the signal to improve the TF energy concentration. Simulation data demonstrates that the proposed algorithm has higher energy aggregation and better noise immunity, especially for signals with cross-IFs. Applying the proposed method to animal acoustic and radar wave signals of pedestrians can accurately describe the differences in the frequency change patterns and the temporal distribution of energy in the signals, thereby providing a judgment basis for effectively identifying and classifying the signals.