Second-Order Transient-Extracting Generalized Warblet Transform Optimized by FrVMD

The generalized Warblet transform (GWT), which employs the Fourier series as the transform kernel function, is suitable for analyzing strong time-varying frequency-modulated signals that change rapidly with time and has a wide range of signal processing applications. However, its time–frequency representation is not sufficiently ideal, and not suitable for high-precision time–frequency analysis applications. To address this issue, we propose a second-order transient-extracting generalized Warblet transform (STEGWT) based on fractional Fourier transform optimization of variational mode decomposition (FrVMD), named FrVMD-STEGWT. This method utilizes the FrVMD method for signal decomposition and reconstruction to eliminate false and meaningless intrinsic mode components, thereby filtering out interfering noise to some extent. Subsequently, second-order transient-extracting transform (STET) is performed on the GWT to improve its time–frequency analysis quality. Experimental results indicate that the FrVMD-STEGWT method effectively enhances the time–frequency concentration and noise resistance of signals, and restores the true time–frequency distribution of multicomponent signals. The application of the FrVMD-STEGWT method to bat sample signals and bearing fault vibration signals achieves high time–frequency analysis concentration, highlighting the validity and utility of this method for high concentration time–frequency analysis applications.