WignerVilledistributionen

The Wigner-Ville distribution, often abbreviated as WVD, is a time-frequency representation of a signal. It was developed by Eugene Wigner in 1932 and later extended to signal processing by Ville in 1948. Unlike simple spectrograms, the WVD provides a representation with higher time-frequency resolution, theoretically being able to capture instantaneous frequencies and their evolution over time.

The Wigner-Ville distribution is a bilinear transformation, meaning it is quadratic in the signal amplitude. This quadratic nature gives rise to the characteristic cross-terms, also known as interference terms, which can appear between different frequency components of the signal. These cross-terms can sometimes make the interpretation of the WVD challenging, as they do not correspond to actual signal components but rather to their interactions.

Mathematically, the WVD of a signal x(t) is defined as the Fourier transform of its ambiguity function. The ambiguity function, in turn, is related to the signal's autocorrelation function. The WVD is particularly useful in analyzing non-stationary signals, where the signal's spectral content changes over time. Applications can be found in areas such as radar signal processing, sonar, biomedical signal analysis, and quantum mechanics. Despite its advantages in resolution, the presence of cross-terms has led to the development of smoothed pseudo-Wigner-Ville distributions and other variations to mitigate these artifacts.