High-Dimensional Synchrosqueezing Chirplet Transform for Analyzing Signals With Multiple Nonproportional Frequencies
Dezun Zhao, Honghao Wang, Lingli Cui
Abstract
It is a challenging issue to characterize nonstationary signals with multiple nonproportional instantaneous frequencies (IFs), especially signals with crossing IFs. Therefore, a novel time-frequency analysis (TFA) algorithm, called high-dimensional synchrosqueezing chirplet transform (HDSCT) is proposed. In the HDSCT, a new dimension called chirp rate and window length (CRWL), which are introduced from the velocity synchronous linear chirplet transform (VSLCT), is first defined; then a high-dimensional synchrosqueezing operator is constructed based on the three-dimensional domain of time-frequency-CRWL; and finally, the high-dimensional synchrosqueezing operator is employed to achieve high-precision rearrangement of the time-frequency coefficients of the VSLCT in the direction of frequency and CRWL. The main contribution is that different from the conventional synchrosqueezing process which only reassigns energy in the time-frequency domain, the HDSCT characterizes signals in the three-dimensional domain of time-frequency-CRWL, where the multiple nonproportional IFs, especially crossover IFs are separated. The performance of the HDSCT is validated by a simulation signal with crossing IFs, a planetary gearbox vibration signal, a killer whale signal, and a bat signal. The comparison with several state-of-the-art TFA methods further illustrates that the HDSCT has a much better performance in dealing with nonstationary signals with multiple nonproportional frequencies, especially signals with crossover IFs.