Time-Frequency Analysis Method: Wigner-Ville Distribution (WVD)

Wigner-Ville Distribution (WVD) is a classical time-frequency analysis method particularly suitable for analyzing instantaneous frequency characteristics of non-stationary signals. It represents signal energy distribution through joint time-domain and frequency-domain representation, providing higher time-frequency resolution compared to Short-Time Fourier Transform (STFT).

Core Principle: WVD essentially constitutes the Fourier transform of the signal's autocorrelation function. Its bilinear characteristic enables precise reflection of signal energy concentration in the time-frequency plane. For single-component signals, WVD forms distinct ridge patterns in the time-frequency representation; however, for multi-component signals, cross-term interference becomes a significant challenge.

MATLAB Implementation Highlights: MATLAB's time-frequency toolbox (such as `tftoolbox`) provides built-in WVD computation functions, typically requiring signal preprocessing to avoid edge effects. Key considerations include window function selection for cross-term suppression and subsequent optimization using improved methods like Smooth Pseudo Wigner-Ville Distribution (SPWVD). In implementation, the `wvd()` function accepts signal vectors and optional parameters for window length and sampling frequency, while `pwvd()` offers pseudo-WVD with enhanced cross-term control through smoothing kernels.

Application Scenarios: Time-frequency localization of impact components in rotating machinery fault diagnosis Instantaneous frequency tracking in radar signal analysis Fundamental frequency extraction in speech signal processing

Limitations: Although WVD theoretically offers optimal time-frequency concentration, practical applications require balancing cross-term suppression with time-frequency resolution. For complex signals, it's often necessary to combine with other methods (like reassignment techniques) to improve readability. Advanced implementations may incorporate adaptive kernel designs or post-processing algorithms to mitigate interference components while preserving signal integrity.