High-Dimensional Synchrosqueezing Chirplet Transform for Analyzing Signals With Multiple Nonproportional Frequencies

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 CT (VSLCT), is first defined; then, a high-dimensional synchrosqueezing operator is constructed based on the 3-D 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 3-D 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.