The on-axis intensity distribution, or the Strehl ratio versus defocus, is described in a phase-space domain in terms of the Wigner distribution function. A coordinate transformation that is defined for a general annular aperture is employed to convert the pupil amplitude transmittance into a one-dimensional function. We show that the single display of the Wigner distribution function associate...

a new derivation of the quantum boltzmann transport equation for the fermion system from the quantum time evolution equation for the wigner distribution function is presented. the method exhibits the origin of the time - irreversibility of the boltzmann equation. in the present work, the spin dependent and indistinguishibility of particles are also considered.

The on-axis image irradiance obtained from a radially symmetric optical system under broadband illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying on-axis irradiance can be derived from different slices of a two-dimensi...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

This paper is concerned with a synthesis study of the fast Fourier transform (FFT), the short time Fourier transform (STFT and the Wigner distribution (WD) in analysing the phonocardiogram signal (PCG) or heart cardiac sounds.     The FFT (Fast Fourier Transform) can provide a basic understanding of the frequency contents of the heart sounds. The STFT is obtained by calculating the Fourier tran...

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...

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...

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε the Wigner function evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/ √ t, for the energy current correlation in equilibrium. This is in agreem...