Time-Extracting Wavelet Transform for Characterizing Impulsive-Like Signals and Theoretical Analysis
Abstract
In this paper, a high-resolution time-frequency (TF) analysis method, called time-extracting wavelet transform (TEWT) is introduced to analyze impulsivelike signals whose TF ridge curves are nearly perpendicular to the time axis. For impulsive-like signals, the instantaneous frequency with almost infinite rate of change is difficult to estimate, but the group delay (GD) with nearly zero rate of change is easier to estimate. Since the GD is the key feature of frequency-domain signals, it indicates that one can try to understand impulsive-like signals from the perspective of frequency-domain signals. In this regard, for an impulsive signal and its Fourier transform (i.e. the frequency-domain harmonic signal), we propose the TEWT that achieves highly-concentrated TF representations while allowing signal reconstruction, only by retaining the TF energy closely related to TF features of signals, while removing