I. Abstract Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over nonco...

Many commonly used time–frequency distributions are members of the Cohen class. This class is defined for continuous signals, and since time–frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time–frequency distributions that are covariant to time shifts and frequency...

An optimised time-frequency signal analysis software tool is presented here as a MATLAB toolbox. This toolbox is implemented using existing and novel methods for a specific class of Time-Frequency Distributions (TFDs) called quadratic TFDs. This is first applied to a TFD called the Wigner-Ville Distribution (WVD), as all other quadratic TFDs can be represented as a smoothed (in both time and fr...

A phase space representation of the Aharonov-Bohm effect is presented. It shows that the shift of interference fringes is associated to the interference term of the Wigner distribution function of the total wavefunction, whereas the interference pattern is defined by the common projections of the Wigner distribution functions of the interfering beams. * Correspondence address: D. Dragoman, P.O....