Discrete-time Wigner Distribution Research Articles

On alias-free discrete time Wigner distributions for time–frequency analysis of fusion plasma signals: application to JET magnetic activity data

The problem of aliasing in relation to the use of Wigner distributions to process discrete time (DT) non-stationary signals from fusion plasma diagnostics is comprehensively addressed. Three DT Wigner distributions, two of which are alias free (AF), are thoroughly studied and compared, their properties being provided as well as, making use of so-called pseudo-Wigner (p-Wigner) distributions, formulae for their efficient computation. Of the three, one is singled out as that AF form which simultaneously obeys an arguably more complete set of desirable properties for time–frequency distributions and which has a lower computational complexity. Such an AF DT Wigner distribution has been known in quantum mechanics as the rotational Wigner function, where it has been introduced to treat rotation angles and their canonically conjugate angular momenta, whose spectra have the same discrete nature as DT signals. As an illustration of the advantages and shortcomings of each of these three distributions, they are applied to the time–frequency analysis of MHD activity data. Thus, the three DT Wigner distributions, more precisely their p-Wigner counterparts, together with the spectrogram for the sake of comparison, are used to obtain representations in the time–frequency plane of non-stationary events from neoclassical tearing mode (NTM) and toroidal Alfvén eigenmode (TAE) experiments in the JET tokamak. Besides aliasing, the appearance in the time–frequency plane of spurious images due to cross-term interference between different signal components is also discussed. If such undesirable artefacts are generated by negative frequencies interfering with positive frequencies, it is shown that the analytic signal can be of great help in reducing cross-term effects.

Time-frequency images of magnetohydrodynamic phenomena in tokamak plasmas using a discrete-time Wigner distribution

A discrete-time Wigner distribution is used to yield a time-frequency representation of nonstationary magnetic activity at the edge of a tokamak plasma, thereby contributing to the magnetohydrodynamic analysis of the underlying phenomena, more precisely, to the identification of toroidal Alfven eigenmodes.

A note on "An overview of aliasing errors in discrete-time formulations of time-frequency representations"

Various realizations asserting to produce the alias-free discrete-time Wigner distribution have been reviewed and analyzed by Costa and Boudreaux-Bartels (see ibid., vol.47, no.5, p.1463-74, May 1999). Here, a simple alias-free form of the pseudo-Wigner distribution is proposed. It is obtained from the fact that the sampled signal can formally be considered as a multicomponent signal.

A contribution to the unaliased discrete-time Wigner distribution

This paper presents a new closed form analytical definition of the unaliased discrete-time Wigner distribution (DTWD), which arises naturally from its continuous-time counterpart, and is straightforwardly implementable for digital signal processing. This DTWD possesses properties that resemble those of the continuous time case. It is shown that this DTWD is the sum of two terms, designated as the even and odd terms, that has interesting symmetric properties similar to those of the discrete Fourier transform. Moreover, this DTWD captures important features of the continuous-time case, and it collapses to the power spectral density function when smoothed with the proper functions. These smoothing functions are limited to be separable. The unaliasedness is validated by computer simulations.

Phase matching algorithms for Wigner-distribution signal synthesis

Signal processing by means of discrete-time Wigner distribution requires a signal synthesis step which contains a troublesome phase ambiguity. The authors analyze the problem of phase ambiguities for unconstrained and halfband-constrained signal synthesis and discuss various strategies for coping with it. After a review of the phase-matching algorithm using a reference signal, the authors present autonomous phase-matching algorithms which do not require a reference signal. Online versions of both reference-based and autonomous phase-matching algorithms which feature a short-time or causal mode of operation and are thus suited for the online processing of signals with arbitrary length are derived. The performance of the algorithms is assessed by computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Synthesis of discrete-time signals from distributions

With minor modification, Sussman&apos;s algorithm is demonstrated to be directly applicable to the problem of leastsquares synthesis of the discrete-time Wigner distribution, provided that it is appropriately defined.