Utilizing the Shift-Invariant Wavelet Packet Decomposition (SIWPD), various useful properties relevant to time-frequency analysis, including high energy concentration and suppressed interference terms, can be achieved simultaneously in the Wigner domain. A prescribed signal is expanded on its best basis and transformed into the Wigner domain. Subsequently, the interference terms are eliminated ...

New method of observation and diagnosis of inverter-fed induction motor drives is developed and tested. Unsymmetrical conditions concerning the machine impedances or valves operation are reflected in the spectrum of the current space-phasor. The spectrum of the space-phasor was estimated with the help of the Wigner-Ville distribution (WVD) and its time-frequency representation with excellent ti...

A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained information. A method is studied for calculating a Wigner distribution from the joint probability distribution obtained in a joint measurement. 1 Quantum tomograph...

The Wigner Distribution (WD) is a bilinear signal transformation possessing several properties that are useful in time-frequency signal analysis. Fast Fourier transform (FFT) techniques have been used to approximate the WD. However, the signal must be sampled at twice the Nyquist rate in order to avoid aliasing errors. This paper deomonstrates that implicit spline interpolation of a continuous ...

This invited paper – of a tutorial and review character – presents an overview of two classes of time-frequency signal representations. The first class, in which the signal arises linearly, deals with the windowed Fourier transform and its sampled version (also known as the Gabor transform) and the inverse of the latter: Gabor’s signal expansion. We will show how Gabor’s signal expansion and th...

A method for time-frequency signal analysis is presented. Theproposed method belongs to the general class of smoothed pseudo Wignerdistributions. It is derived from the analysis of the Wigner distributiondefined in the frequency domain. This method provides some substantialadvantages over the Wigner distribution. The well-known cross termeffects are reduced or completely rem...

A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary cl...

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian ope...

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a ⋆-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability ...

We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.