A time-frequency distribution provides many advantages in the analysis of multicomponent nonstationary signals. The simultaneous signal representation with respect to the time and frequency axis defines the signal amplitude, frequency, bandwidth, and the number of components at each time moment. The Rényi entropy, applied to a time-frequency distribution, is shown to be a valuable indicator of ...

A method for reducing the cross-terms in the WD with an adaptive frequency smoothing window is proposed in this paper. By using the short time Fourier spectrum of the input signal and some simple preprocessing steps, such as smoothing and peak labeling, the proposed method adaptively calculates the width of the frequency smoothing window. The simulation results of the linear frequency modulated...

G. Harder,1 Ch. Silberhorn,1, 2 J. Rehacek,3 Z. Hradil,3 L. Motka,3 B. Stoklasa,3 and L. L. Sánchez-Soto4, 2 1Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany 2Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany 3Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech R...

Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are investigated in terms of geometric positive trace increasing maps (PTI), for general 1D domains, as well as 2D shapes e.g. circles, disks. Spectral properties ...

Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum–Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its ...

Moments of a Wigner distribution are defined based on both the space and spatial frequency coordinates and are considered as a summarization of the distribution. A method is proposed in this paper to derive functions called affine Wigner moment invariants (AWMI) based on these moments. These functions remain unchanged when the underlying images are affine transformed. As Wigner distributions co...

Basic computational aspects of the Wigner function approach for modeling and simulation of electronic transport are discussed, beginning with the coherent problem, followed by the dissipative problem including scattering events, which has been recently restated in terms of a scattering-induced Wigner function correction. These alternative formulations of the computational task are discussed alo...

We quantize non-commutative QED canonically in the background field gauge for weak and slowly varying background fields. We determine the complete basis for expansion under such an approximation. As an application, we derive the Wigner function which determines the leading order high temperature behavior of the perturbative amplitudes of non-commutative QED. To leading order, we also give a clo...

2014 We study the fission dynamics from the region of the saddle point to the scission configuration. For this we solve an équation of Fokker-Planck type for a multi-dimensional Wigner function. This équation accounts for dissipative as well as quantal features. We study the influence of the initial condition as well as friction and diffusion coefficients on the final values for the variances o...

We characterize the Schwartz space of rapidly decaying test functions by the decay of the short-time Fourier transform or cross-Wigner distribution. Then we prove a version of Hardy’s theorem for the short-time Fourier transform and for the Wigner distribution.