Wigner-Ville Distribution (WVD) - Time-Frequency Signal Analysis Technique

The Wigner-Ville Distribution (WVD) is a fundamental mathematical tool in signal processing and time-frequency analysis. Originally introduced by Eugene Wigner in 1932, this distribution represents signal energy as a joint function of both time and frequency variables. The WVD is particularly valuable due to its exceptional time-frequency resolution, outperforming traditional methods like Short-Time Fourier Transform in many applications. From an implementation perspective, the WVD can be computed using the formula: WVD(t,ω) = ∫ x(t + τ/2) · x*(t - τ/2) · e^(-jωτ) dτ, where x(t) represents the analytic signal and x*(t) denotes its complex conjugate. This quadratic time-frequency distribution requires careful handling of cross-term artifacts when analyzing multi-component signals. Key applications include speech processing where it helps visualize formant transitions, radar signal analysis for detecting time-varying frequency modulations, and biomedical signal processing for analyzing non-stationary physiological signals. In MATLAB implementation, researchers often use built-in functions or custom scripts to compute WVD, typically involving Hilbert transform for analytic signal generation followed by the core distribution calculation. The distribution's ability to reveal intricate signal patterns makes it indispensable for analyzing non-stationary signals where frequency content evolves over time. Despite its computational complexity and cross-term challenges, the WVD remains a powerful tool across various engineering and scientific disciplines, particularly when high time-frequency localization is required.