An energy-concentrated wavelet transform for time-frequency analysis of transient signal

Some signals captured in practical applications are usually composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), i.e., transient signal, which enables some advanced time-frequency analysis (TFA) tools no longer ideal or even ineffective. Fortunately, the group delay (GD) of such signal can be well expressed as a single valued function of frequency. By considering frequency-domain signal model suitable for describing GD, we develop a postprocessing technique called wavelet transform (WT)-based time-reassigned synchrosqueezing transform (WTSST). In WTSST, the TF coefficients diffused in WT are gathered to GD of transient signal aiming to generate a more concentrated time-frequency representation (TFR) and WTSST allows to retrieve the whole or part of signal. Considering analytic WT under Gaussian function, the theoretical analyses of WTSST are provided, which includes the analyses of GD candidate accuracy and signal reconstruction accuracy. Moreover, based on the theoretical analyses of WTSST, the WT-based time-reassigned multisynchrosqueezing transform (WTMSST) is proposed by introducing a fixed-point iteration scheme, which further improves the shortcoming that WTSST is unable to accurately describe strong frequency-varying signal. Simulation and real signal analyses illustrate that the proposed method has capacity to appropriately describe the features of transient signals.