Synchroextracting chirplet transform for accurate IF estimate and perfect signal reconstruction

Synchroextracting transform (SET) is a recently developed time-frequency analysis (TFA) method aiming to achieve a highly concentrated TF representation. However, SET suffers from two drawbacks. The one is that SET is based upon the assumption of constant amplitude and linear frequency modulation signals, therefore it is unsatisfactory for strongly amplitude-modulated and frequency-modulated (AM-FM) signals. The other is that SET does not allow for perfect signal reconstruction, which leads to large reconstruction errors when addressing fast-varying signals. To tackle these problems, in this paper, we first present some theoretical analysis for the SET method, including the existence of the fixed squeeze frequency, the performances of the instantaneous frequency (IF) estimator and the SET reconstruction. Then, a new TFA method, named synchroextracting chirplet transform (SECT), is proposed, which sharpens the TF representation by extracting the TF points satisfying IF equation, and retains an excellent signal reconstruction ability. Numerical experiments on simulated and real signals demonstrate the effectiveness of the SECT method.