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 ad-vanced 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. Consider-ing 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 the-oretical analyses of W TSST, the W T-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 anal-yses illustrate that the proposed method has capacity to appropriately describe the features of transient signals.