Related papers: Linear perturbations of the Wigner distribution an…
In this note we exhibit recent advances in signal analysis via time-frequency distributions. New members of the Cohen class, generalizing the Wigner distribution, reveal to be effective in damping artefacts of some signals. We will survey…
We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner…
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literature. Some of these are recalled in the Introduction. In this…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
The quadratic nature of the Wigner distribution causes the appearance of unwanted interferences. This is the reason why engineers, mathematicians and physicists look for related time-frequency distributions, many of them are members of the…
The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
We prove a formula expressing the gradient of the phase function of a function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency moment of the Wigner distribution for fixed time. The formula holds when $f$ is the Fourier…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with…
In this work, we investigate the microlocal properties of the evolutions of Schr\"odinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaplectic Wigner distributions, satisfying particular…
The usefulness of time-frequency analysis methods in the study of quasicrystals was pointed out in a previous paper, where we proved that a tempered distribution $\mu$ on ${\mathbb R}^d$ whose Wigner transform is a measure supported on the…
One of the most popular time-frequency representation is certainly the Wigner distribution. To reduce the interferences coming from its quadratic nature, several related distributions have been proposed, among which the so-called…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
We investigate the $\tau$-quantizations and Cohen's class distributions of a suitable class of trace-class operators, called Feichtinger's operators, and show that it is a convenient substitute for the class of Schwartz operators. Many…
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which…
Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the…
I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…