Theoretical analysis of time-reassigned synchrosqueezing wavelet transform. (October 2022) - Li, Wenting; Zhang, Zhuosheng; Auger, François; Zhu, Xiangxiang
Abstract: In this letter, we first propose a time-reassigned synchrosqueezing wavelet transform (TSWT) to analyze impulsive-like signals, whose instantaneous frequency curves are nearly perpendicular to the time axis. By squeezing the wavelet transform coefficients in the time direction, the TSWT has very high energy concentration and enables signal reconstruction. Furthermore, we provide a rigorous theoretical analysis of TSWT for frequency-domain signals under the mathematical framework. Finally, numerical experiments are employed to verify the effectiveness of TSWT. Highlights: We introduce a high-resolution time–frequency analysis method called time-reassigned synchrosqueezing wavelet transform (TSWT) to analyze impulsive-like signals. We define a class of frequency-domain harmonic-like signal model. We develop a theoretical analysis of TSWT for frequency-domain signals. For impulsive-like signals, TSWT achieves highly-concentrated time frequency representations while allowing signal reconstruction.