Synchroextracting Transform

TLDR: The main idea of SET is to only retain the TF information of STFT results most related to time-varying features of the signal and to remove most smeared TF energy, such that the energy concentration of the novel TF representation can be enhanced greatly.

Abstract: In this paper, we introduce a new time-frequency (TF) analysis (TFA) method to study the trend and instantaneous frequency (IF) of nonlinear and nonstationary data. Our proposed method is termed the synchroextracting transform (SET), which belongs to a postprocessing procedure of the short-time Fourier transform (STFT). Compared with classical TFA methods, the proposed method can generate a more energy concentrated TF representation and allow for signal reconstruction. The proposed SET method is inspired by the recently proposed synchrosqueezing transform (SST) and the theory of the ideal TFA. To analyze a signal, it is important to obtain the time-varying information, such as the IF and instantaneous amplitude. The SST is to squeeze all TF coefficients into the IF trajectory. Differ from the squeezing manner of SST, the main idea of SET is to only retain the TF information of STFT results most related to time-varying features of the signal and to remove most smeared TF energy, such that the energy concentration of the novel TF representation can be enhanced greatly. Numerical and real-world signals are employed to validate the effectiveness of the SET method.