Generalized Synchrosqueezing Transform: Algorithm and Applications

Time-frequency analysis (TFA) is a vital method to deal with nonstationary signals. However, the traditional TFA methods cannot produce a concentrated time-frequency representation (TFR) for the nonstationary signal with strongly time-varying instantaneous frequency (IF). In this work, a new TFA method named generalized synchrosqueezing transform is proposed to deal with the nonstationary signal with complicated IF. First, the explicit formula of the high-order IF estimation is calculated by a new computational framework. Next, the generalized synchrosqueezing operator (GSSO) is constructed by iterative operations. After that, the time-frequency energy is rearranged according to the constructed GSSO to obtain a more concentrated TFR. Finally, the efficient algorithm implementation is introduced to show the feasibility of the proposed method. Numerical data are used to demonstrate the effectiveness and superiority of the proposed method in improving the concentration and accuracy of the TFR of the nonstationary signal with complex IF. Experimental validation proves that the proposed method is effective in analyzing real-world signals and fault diagnosis.