Generalized synchroextracting transform: Algorithm and applications

Time-frequency (TF) rearrangement methods represented by synchrosqueezing transform (SST) and synchroextracting transform (SET) have recently been considered efficient tools for obtaining time-varying features of nonstationary signals. However, so far improving concentration and accuracy is still an open problem, especially for the signal with strongly time-varying instantaneous frequency (IF), due to the fact that they cannot achieve an accurate and generalized IF estimation. In order to address this problem, we introduce a new TF analysis method termed as generalized synchroextracting transform (GSET) by constructing a general signal model. Our first contribution in this study is proposing a new computational framework to derive the generalized explicit formula of Nth-order IF estimation, which can realize the programming of any order IF. By extracting the energy of the TF representation (TFR) on the estimated IF, a more concentrated and accurate TFR can be obtained. Our second contribution is giving a more accurate signal reconstruction method of the TFR from a new perspective. It solves the problem that the reconstruction method of the synchroextracting transform cannot be extended to the Nth-order. Numerical analysis of multicomponent simulated signal demonstrates that the GSET can effectively improve the TF readability of strongly time-varying signal and accurately reconstruct the signal from the TFR. Moreover, experiment and application results verify that the proposed method can be used for fault diagnosis of rotating machinery.