Adaptive Local Maximum Synchrosqueezing Transform via Adaptive Window With Time-Varying Function and Time- Varying Searching Region

Since time–frequency (TF) analysis can provide TF information for characterizing the time-varying signals, TF analysis is a powerful tool for analyzing the nonstationary (N-S) signals. An important task of TF analysis is to yield a sharp TF representation that energy distribution is highly concentrated at an instantaneous frequency (IF) in the TF plane. In order to yield concentrated TF representation on the premise of signal reconstruction, this article proposes a local maximum synchrosqueezing transform (LMSST)-based TF analysis method with time-varying window and time-varying searching region. In particular, the adaptive window with the time-varying function is employed to suppress the violation produced by time-varying frequency characteristics. Here, the time-varying function is optimized based on the local Rényi entropy. Also, the local maximum of the TF coefficients is computed within the time-varying region to be the estimator of the IF of the signals. The time-varying region is employed to match different kinds of signals. In the meantime, it is proved that the signals can be reconstructed. The computer numerical simulation results show that our work yields sharper TF representation than the existing methods. Also, reconstructed signals are closer to the origin signals. In addition, the effectiveness of the proposed method is validated on real-world signals that contain the stationary signals and the N-S signals.