Newton Time-Reassigned Multi-Synchrosqueezing Wavelet Transform

Abstract

In this letter, we introduce an accurate group delay estimator and two high-resolution time-frequency analysis methods to characterize fast frequency-varying signals. Firstly, we explore the limitations of time-reassigned synchrosqueezing wavelet transform and its multi-synchrosqueezing case in dealing with fast frequency-varying signals. Secondly, we present Newton group delay estimator based on wavelet transform properties and Newton's method. Based on this, we introduce the Newton time-reassigned synchrosqueezing wavelet transform, which improves the readability of the time-frequency representation, by reassigning the wavelet transform coefficients into the group delay trajectories along the time direction, and further derive its reconstruction formula. Moreover, we propose Newton time-reassigned multi-synchrosqueezing wavelet transform by multiple squeezing operations, which can achieve a more concentrated time-frequency representation and accurate signal reconstruction. Finally, we employ synthetic and real signals to verify the effectiveness of the proposed methods on the time-frequency energy concentration, group delay estimation and signal reconstruction.