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

TL;DR

This paper introduces a wavelet transform-based synchrosqueezing method for high-resolution time-frequency analysis of transient signals, effectively capturing multivalued instantaneous frequencies and improving signal reconstruction.

Contribution

The paper proposes the WTSST and WTMSST methods that embed a group delay operator into synchrosqueezing, enhancing energy concentration and handling strong frequency variations in transient signals.

Findings

High energy concentration in time-frequency representation

Effective retrieval of transient signal components

Improved analysis of frequency-varying signals

Abstract

Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of such signal can be well expressed as a single valued function of frequency. By considering the frequency-domain signal model, we present a postprocessing method called wavelet transform (WT)-based time-reassigned synchrosqueezing transform (WTSST). Our proposed method embeds a two-dimensional GD operator into a synchrosqueezing framework to generate a time-frequency representation (TFR) of transient signal with high energy concentration and allows to retrieve the whole or part of the signal. The theoretical analyses of the WTSST are provided, including the analysis of GD candidate accuracy and signal reconstruction accuracy. Moreover, based on WTSST, the WT-based time-reassigned multisynchrosqueezing transform (WTMSST) is proposed by introducing a stepwise refinement scheme, which further improves the drawback that the WTSST method is unable to deal with strong frequency-varying signal. Simulation and real signal analysis illustrate that the proposed methods have the capacity to appropriately describe the features of transient signals.