WignerVillesignaali

WignerVillesignaali, or the Wigner–Ville signal, refers to a time–frequency representation used in signal processing to analyze non-stationary signals. It aims to provide a high-resolution view of how a signal’s frequency content evolves over time.

The core concept is the Wigner–Ville distribution (WVD) of a signal x(t), defined as W_x(t,f) = ∫ x(t+τ/2) x*(t−τ/2) e^{−j 2π f τ} dτ. This bilinear form combines time and frequency information to localize signal components more precisely than many linear transforms. Marginal properties hold: ∫ W_x(t,f) df = |x(t)|^2 and ∫ W_x(t,f) dt = |X(f)|^2, where X(f) is the Fourier transform of x(t). The distribution is real-valued but not guaranteed to be nonnegative, and it is known for potential cross-terms.

A key limitation is the appearance of cross-terms when the signal has multiple components, which can create interference patterns in the time–frequency plane and complicate interpretation. Various approaches, such as smoothing kernels in Cohen’s class, kernelized distributions, and reassignment or synchrosqueezing techniques, are used to mitigate cross-terms while preserving resolution.

Applications of Wigner–Ville analysis include speech and music signal processing, radar and sonar, and other non-stationary signal analyses where precise time–frequency localization is valuable. The method has historical roots in work by Eugene Wigner and Jean Ville and remains a foundational tool in time–frequency analysis.