We examine the affine Wigner distribution from a quantization perspective with an emphasis on underlying group structure. One of our main results expresses scalogram as (affine) convolution distributions. strive to unite literature distributions and we provide connection Mellin transform in rigorous manner. Moreover, present ambiguity function show how this can be used illuminate properties dis...

The application of Wigner distribution (WD)-based signal synthesis to signal separation problems is often adversely affected by WD interference terms. We present a modified signal synthesis method where the use of a masked WD allows the definition of don’t-care regions. In the don’t-care regions, detrimental interference terms (whose timefrequency location is assumed to be known) are ignored. T...

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε the local spectral density (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 equil...

The Wigner-Ville Distribution (WVD) and Pseudo-Wigner-Ville Distribution (PWVD) are very popular and effective methods for detecting Linear Frequency Modulated (LFM) signals in noisy environments. Hough transform is also widely used method for detection and parameter estimation of chirp signals. However, when there are signals with very different strength from each other, it is difficult to sim...

We present a review of the applications of the Wigner distribution function in various areas of signal processing: amplitude and phase retrieval, signal recognition, characterization of arbitrary signals, optical systems and devices, and coupling coefficient estimation in phase space. Although reference is made to specific signals and systems, the mathematical formulation is general and can be ...

The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function which reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the...

Wigner Distribution, one of many methods to compute time frequency representation, satisfies large number of mathematical properties and gives optimal energy concentration in time frequency plane. However, Wigner distribution suffers from severe cross-term interference problem, which limits its scope for practical applications. Different modified versions of Wigner distribution have been develo...

The connection between the instantaneous frequency and the angle derivative of the fractional power spectra is established. It permits to solve the signal retrieval problem if only two close fractional power spectra are known. This fact is used in the reconstruction of the Wigner distribution or the pseudo Wigner distribution from two close projections. Keywords—Wigner distribution, fractional ...

The present paper establishes the self-averaging, radiative transfer limit for the twofrequency Wigner distribution for random classical waves in the paraxial approximation. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmannlike integral equation or a Fokker-Planck-like differential equation in the phase space. When the longitudinal fl...