Gaussian-modulated linear group delay model: Application to second-order time-reassigned synchrosqueezing transform

This paper considers the analysis of impulsive-like signals whose time-frequency ridge curves are nearly perpendicular to the time axis. Although the instantaneous frequency of such a signal is a multivalued time-dependent function, its group delay is a single-valued function of frequency, which indicates that a frequency-domain signal model is more suitable for describing impulsive-like signals. Therefore, a new frequency-domain signal model, called Gaussian-modulated linear group delay (GLGD) model, is applied to the second-order time-reassigned transform (TSST2) that achieves the time-frequency representation (TFR) of impulsive-like signals while allowing mode decomposition. Compared to the recently proposed time-reassigned synchrosqueezing transform (TSST), the TSST2 can provide a more accurate group-delay estimator, which is beneficial to obtain a sharper TFR. Numerical signals and experimental signals are employed to validate the effectiveness of the proposed TSST2.