Local Maximum Synchroextracting Transform Based on Time-Varying Window

Time frequency (TF) representation has been applied in many fields. An essential task of TF representation is to clearly present instantaneous frequency (IF) trajectories of analytic signals in the TF plane. With proper mathematical reasoning, it can be learned that IF of analytic signal should be anticipated to reach the peak value of TF energy in the frequency direction at a specific time index. For multicomponent signals, IF is expected to align with a local maximum of TF energy in the frequency direction at a specific time index. Therefore, local maximum-based post-processing methods have garnered significant attention for achieving TF representation with a high degree of concentration. Nonetheless, time-invariant window with predefined parameter cannot simultaneously satisfy signals with frequency-varied characteristic and harmonic signals, which results in negative effect that local maximum may not be matched with IF in the frequency direction for various kinds of signals. In this study, a local maximum synchroextracting transform based on a time-varying window is proposed. In the proposed method, TF coefficients on IF trajectories can be retained by rules based on properties of local maximum, while diffused region in the TF plane can be removed. In order to suppress above negative effect of time-invariant window, time-varying variance \(\sigma (t)\) and time-varying chirp rate \(\beta (t)\) are adaptively estimated based on the local Rényi entropy for accurate IF estimation. Finally, highly energy-concentrated TF representation can be obtained. In the meantime, signal reconstruction of the proposed method is proven. Computer numerical simulation shows that the proposed method is superior to the compared TF analysis methods.