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Transient signals are often composed of a series of modes that havemultivalued time-dependent instantaneous frequency (IF), which bringschallenges to the development of signal processing technology. Fortunately, thegroup delay (GD) of such signal can be well expressed as a single valuedfunction of frequency. By considering the frequency-domain signal model, wepresent a postprocessing method called wavelet transform (WT)-basedtime-reassigned synchrosqueezing transform (WTSST). Our proposed method embedsa two-dimensional GD operator into a synchrosqueezing framework to generate atime-frequency representation (TFR) of transient signal with high energyconcentration and allows to retrieve the whole or part of the signal. Thetheoretical analyses of the WTSST are provided, including the analysis of GDcandidate accuracy and signal reconstruction accuracy. Moreover, based onWTSST, the WT-based time-reassigned multisynchrosqueezing transform (WTMSST) isproposed by introducing a stepwise refinement scheme, which further improvesthe drawback that the WTSST method is unable to deal with strongfrequency-varying signal. Simulation and real signal analysis illustrate thatthe proposed methods have the capacity to appropriately describe the featuresof transient signals.

An Energy-concentrated Wavelet Transform for Time Frequency Analysis of Transient Signals