Fundamentals of Wigner-Ville Distribution

In this article, we will explore the fundamentals of Wigner-Ville Distribution (WVD) using a composite signal as an example. The Wigner-Ville Distribution serves as an important time-frequency analysis tool that enables the determination of instantaneous frequency and power spectral density of signals. When implementing WVD, signals must be transformed into the time-frequency domain, typically achieved through mathematical operations involving the signal's analytic representation and its time-delayed versions. The core algorithm involves computing the Fourier transform of the product between the signal and its time-reversed, complex-conjugated version across different time delays. In practical implementations, this requires careful handling of cross-term interference, which is characteristic of quadratic time-frequency distributions. Code implementation typically involves windowing techniques and proper sampling strategies to mitigate artifacts. WVD provides superior time-frequency localization compared to linear transforms like STFT, making it particularly valuable for analyzing non-stationary signals. The resulting time-frequency representations offer crucial insights into signal characteristics, with applications spanning wireless communications, medical imaging analysis, and advanced signal processing. After performing the basic Wigner-Ville distribution, we obtained significant results that facilitate further investigation of signal properties. These outcomes contribute to deeper understanding of complex signal behaviors, with implementation considerations including computational efficiency optimization and cross-term reduction techniques for practical applications.