Synchroextracting Transform

TLDR

Time‑frequency analysis requires accurate time‑varying information such as instantaneous frequency, and the synchrosqueezing transform squeezes coefficients onto the IF trajectory, inspiring the new synchroextracting transform. The paper introduces a new time‑frequency analysis method to study trend and instantaneous frequency of nonlinear, nonstationary data. SET is a post‑processing of the short‑time Fourier transform that selectively retains TF components linked to time‑varying features while discarding smeared energy, thereby enhancing energy concentration, and its effectiveness is validated on numerical and real‑world signals. Compared with classical TFA methods, SET produces a more energy‑concentrated time‑frequency representation and enables signal reconstruction.

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.