In this study, we proposed a joint time-frequency distribution of suppressing cross-terms aiming at cross-terms interference of Wigner-Ville distribution. According to the analyzed signal, the Wigner-Ville distribution and Smooth Pseudo Wigner-Ville distribution can be obtained. Moreover, the prototype of timefrequency distribution can be obtained by non-linear filter for Smooth Pseudo Wigner-V...

Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration in the frequency domain allows the determination of near-field diffraction, leading to the well known Fresnel diffraction when small angles are considered an...

The rigorous quantum mechanical definition of a resonance requires determining the pole position in the second Riemann sheet of the analytically continued partial wave scattering amplitude in the complex Mandelstam s variable plane. For meson resonances we investigate the alternative Breit-Wigner (BW) definition within the large NC expansion. By assuming that the pole position is O(N C) and exp...

We present the reconstruction of the Wigner function of a classical phasesensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid photodetector operated above its photon-resolving regime, we obtained both the statistics at different values of the probe field and the values of the probe ...

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non-classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable qu...

We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function is asymptotically given by the Airy kernel, thereby generalizing the well-known result for the Gaussian Unitary Ensemble (GUE). Moreover, we obtain similar ...

The integral of the Wigner function over a subregion of the phasespace of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over all possible states, reduces to the problem of finding the greatest and least eigenvalues of an hermitian operat...

The four-dimensional Wigner distribution function is determined from intensity profiles measured in the focused photon beam of FLASH (Free-electron laser in Hamburg) for a variety of photon beamline settings. The Wigner formalism results in comprehensive coherence information without the requirement of simplifying assumptions on the beam. The entire four-dimensional spatial mutual coherence fun...

The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval [0, 1]. The problem of finding bestpossible upper and lower bounds for a given region is the problem of finding the greatest and least eigenvalues of an asso...

The modulation-based time-variant filters are very useful for nonstationary signal processing. They can be constructed by three stages: pre-modulation, time-invariant low-pass filtering and post-modulation. Wigner distribution is a popular tool for showing the time-frequency distribution of nonstationary signals. The combination of these two techniques is presented in this paper. We introduce W...