Generalized Transient-Extracting Transform and Its Accurate Signal Reconstruction

Traditional time–frequency analysis (TFA) methods can effectively obtain instantaneous frequency (IF) features of nonstationary signals by constructing the signal model in the time domain. However, they fail to deal with the transient signal because the IF of the transient signal is discontinuous in the time domain and is a multivalued function with respect to time. Thus, in this article, we introduce a new TFA method, termed generalized transient-extracting transform (GTET), to obtain sharper time–frequency representation (TFR) of the transient signal by constructing frequency-domain model. First, we propose a new computational framework for group delay (GD). By deriving the general explicit formula for the
N
th-order GD, the programming implementation of any order GD can be achieved. Next, the concentrated TFR of GTET can be generated by extracting the energy from the generalized GD estimation. Finally, the signal reconstruction of GTET is derived from a new perspective. It overcomes the difficulty that the reconstruction method of transient-extracting transform cannot be generalized to high-order algorithms. The analysis result of the simulated signal with high-order GD shows that GTET has better performance than other TFA methods. Experimental results demonstrate that GTET can be used to analyze practical transient signals.