Frequency-Domain Energy-Concentrated Synchrosqueezing Transform for Frequency-Varying Signal With Linear Group Delay

Abstract

Reassigned method (RM) can provide a high energy-concentrated time–frequency representation (TFR) result for the frequency-varying signal with linear group delay by reassigning the TF coefficients among both the time and frequency directions, while the TFR result provided by RM cannot be reconstructed since the reassigned operators in RM are conducted on the absolute short-time Fourier transform (STFT) representation. Time-reassigned synchrosqueezing transform (TSST) is capable of depicting the changing dynamic of the weak frequency-varying signal with perfect signal reconstruction. However, the theoretical assumption in TSST makes it unsuitable to process strong frequency-varying signal. To make the RM result for the frequency-varying signal with linear group delay available for signal reconstruction, a frequency-domain energy-concentrated synchrosqueezing transform is proposed by taking the merits of the two time–frequency analysis (TFA) methods into an integrated whole. In the proposed method, the relationship between the reassigned operators in the RM and the inclination angle of the linear group delay of the frequency-varying signal is first analyzed, and then a new time-reassigned synchrosqueezing operator is formulated by adjusting a time length on the original time reassignment operator in RM on the basis of the estimated inclination angle. The validation results on both the simulated and real-world data highlight that the proposed method can provide a high energy-concentrated TFR result for the frequency-varying signal with linear group delay.