Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing

Synchrosqueezing transform (SST) is an effective post-processing time-frequency analysis (TFA) method in mechanical signal processing. It improves the concentration of the time-frequency (TF) representation of non-stationary signals composed of multiple components with slow varying instantaneous frequency (IF). However, for components whose TF ridge curves are fast varying, or even nearly parallel with frequency axis, the SST still suffers from TF blurs. In this paper, we introduce a TFA method called time-reassigned synchrosqueezing transform (TSST) that achieves highly concentrated TFR for impulsive-like signal whose TF ridge curves is nearly parallel with frequency axis. Moreover, the TSST enables signal reconstruction, compared with the standard TF reassignment methods, such as reassigned short-time Fourier transform and reassigned wavelet transform. In the algorithm of TSST, the group delay estimator is calculated rather than the IF estimator. Furthermore, the TF coefficients are reassigned in the time direction rather than in frequency direction as the SST did. Then we compare the concentration between SST and TSST at different length of Gaussian window and chirp-rate, which is followed by the respective application scope of SST and TSST. Furthermore, we describe an efficient numerical algorithm for practical implementation of TSST. It is found that the SST is suitable for characterizing signal with small chirp-rate while TSST performs better for a large chirp-rate condition. Thus, the TSST is more capable of extracting transient features of impulsive-like signal. Finally, the effectiveness of the TSST and its inverse transform is verified by simulation and experimental studies.