The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein–Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein–Gordon field are derived. It is shown that they lea...

In the continuous-time domain, Maximum-Likelihood (ML) detection of a chirp signal in white Gaussian noise can be done via the line-integral transform of the classical Wigner distribution. The line-integral transform is known variously as the Hough transform and the Radon transform. For discrete-time signals, the Wigner-type distribution defined by Claasen and Mecklenbrauker has become popular ...

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicityfree) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix...

Applying the fractional Fourier transform (FRFT) and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the n-dimensional Wigner distribut...

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity ...

A conditional kinetic energy is defined in terms of the Wigner distribution. It is shown that this kinetic energy may become negative for negative Wigner distributions. A free particle wave packet with negative kinetic energy will spread in a nonclassical manner. 1 The Free Particle In classical statistical mechanics, a particle is described in terms of a nonnegative phase space distribution P ...

The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates theWigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of WignerVille di...