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

Abstract

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.