The Wigner-WeylMoyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space co-ordinate, for example, in terms of a bilinear convolution of two fermionic objects, e.g. a quark antiquark pair. This construction is essentially non-local,...

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This ...

Wigner function(WF), a quasi-probability distribution in phase space, was first introduced to describe quantum state in quantum mechanics by E. P. Wigner[1]. And later, it was extended to classical optics and signal processing. Since its birth, a great number of applications have been conducted in different fields. As for the original quantum case, like a continuous onedimensional quantum syste...

The paper introduces a new kernel for the design of a high resolution time–frequency distribution (TFD). We show that this distribution can solve problems that the Wigner–Ville distribution (WVD) or the spectrogram cannot. In particular, the proposed distribution can resolve two close signals in the time–frequency domain that the two other distributions cannot. Moreover, we show that the propos...

The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this function is given by a sum of three parts: the classical one, the quantum corrections and the contribution due to the opening of the system. In the particular cas...

We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature —in this paper on hyperboloids—, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D, 1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic c...

The Wigner distribution (WD) possesses a number of desirable mathematical properties relevant time-frequency analysis. However, the presence of interference terms renders the WD of multicomponent signals extremely di cult to interpret. In this work, we propose an adaptivedecomposition of the WD using extended libraries of orthonormal bases. A prescribed signal is expanded on a basis of adapted ...

In this study a time-frequency method based on Wigner-Ville Distribution (WVD) is used for detection and parameter estimation of Frequency Modulated Continuous Wave (FM-CW) Radar Signal. The proposed method uses the Pseudo-Wigner-Ville Distribution (PWVD) as a time-frequency detection technique and Radon Transform to identify the parameter of the modulation. The Wigner-Ville Radon Transform (WV...

We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner function (WF) and the correlations of the marginal distribution. We show that a state is entangled if at least one among the values assumed by the corresponding d...

The paper deals with analysis and time-frequency representation of multicomponent signals characterised by non-linear frequency variation in time. A certain type of higher-order time-frequency distribution, referred to as Polynomial Wigner-Ville distribution [2], has been designed to achieve delta function concentration in the timefrequency plane for this class of signals. In the presence of mu...