Second-Order Transient-Extracting Transform With Application to Time-Frequency Filtering

This article introduces the second-order transient-extracting transform (TET2) to extract transient components from a nonstationary signal. Different from the traditional transient-extracting transform (TET1), the proposed method is based on a more general frequency-domain signal model, termed the Gaussian-modulated linear group delay signal model. The first step of the proposed method is the computation of the second-order group delay (GD) estimator that describes the temporal positioning of signal ridges in the time-frequency (TF) plane. Based on this second-order GD estimator, we can then obtain an energy-concentrated TF representation. Finally, the transient component of interest is reconstructed after filtering out the noise in the TF plane. Thus, the TET2 can be considered as an effective TF filtering tool. Numerical experiments on real and synthetic signals show the effectiveness of the proposed method in the TF filtering application.