Time–Frequency-Multisqueezing Transform

In the real world, most signals encountered are nonstationary. It is essential to extract a time-frequency (TF) characteristics in such signals for an accurate description. Two parameters are usually applied to quantify the TF characteristics of a nonstationary signal, i.e., instantaneous frequency (IF) and group delay (GD). A post-processing strategy was adopted by two recently developed techniques, the synchrosqueezing transform (SST) and the time-reassigned SST (TSST) to accurately capture the change rules of IF and GD respectively. However, due to the diversity of modes in complex nonstationary signals, no existing technique has been used to effectively estimate both IF and GD simultaneously. To solve this problem, a post-processing analysis technique termed as time-frequency-multisqueezing transform (TFMST) is proposed in this paper where a so-called chirp rate (CR) discrimination criterion is established by considering the Gaussian window in the short-time Fourier transform. The proposed method can accurately categorize nonstationary signals containing harmonic- and impulsive-like components to achieve a concurrent description and ensure the recovery of original signals. The proposed method is validated by numerical simulation and real signal analyses.