MATLAB Implementation of SPWVD Time-Frequency Analysis with Code Description

The Smoothed Pseudo Wigner-Ville Distribution (SPWVD) is an enhanced time-frequency analysis method that improves upon the traditional Wigner-Ville distribution by incorporating smoothing window functions. This approach effectively suppresses cross-term interference while maintaining high time-frequency resolution, making it particularly valuable for analyzing non-stationary signals in applications such as mechanical fault diagnosis, biomedical signal processing, and vibration analysis. Key implementation steps for SPWVD include signal preprocessing, window function design, time-frequency kernel computation, and final distribution calculation. The implementation typically begins with signal normalization or denoising preprocessing to ensure data quality. Appropriate time-domain and frequency-domain smoothing windows are then selected - these windows independently control the smoothing degree in temporal and spectral directions. The core computation involves calculating the time-frequency kernel by combining the signal with the window functions, ultimately generating the SPWVD distribution. In MATLAB implementation, programmers typically create a main M-file that utilizes built-in FFT functions and other signal processing toolbox components. The code structure often includes parameter configuration for window lengths and types, where longer time-domain windows enhance frequency resolution while shorter windows better capture rapid signal variations. A typical implementation would involve: 1. Signal input and validation using MATLAB's input checking functions 2. Window generation using functions like hamming(), hanning(), or gaussian() 3. Kernel computation through convolution operations and FFT-based spectral processing 4. Visualization using time-frequency images or 3D surface plots via surf() or imagesc() To enhance code reusability, the core SPWVD calculation is often encapsulated into a separate function that accepts customizable parameters for signal data, window options, and resolution settings. This modular approach allows users to easily adapt the algorithm for specific applications. The visualization component is crucial for result interpretation, typically employing color-mapped time-frequency representations or interactive 3D plots that enable intuitive observation of signal characteristics. MATLAB's implementation of SPWVD not only provides practical tools for research and engineering applications but also serves as an educational platform for understanding non-stationary signal properties. Through parameter optimization and algorithm refinement, this method can be extended to handle more complex signal analysis challenges in various domains.