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 the 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 postprocessing strategy was adopted by two recently developed techniques, the synchrosqueezing transform (SST) and the time-reassigned SST 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, in this article, a postprocessing analysis technique termed as TF-multisqueezing transform is proposed, where a so-called chirp rate discrimination criterion is established by considering the Gaussian window in the short-time Fourier transform. The proposed method can accurately categorize non-stationary 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.