The Wigner distribution as a tool for time-frequency analysis of fusion plasma signals: application to broadband reflectometry data

Abstract

The Wigner distribution is introduced as an appropriate tool for processing data from fusion plasma diagnostics whose signals have a time varying frequency spectrum, and is thus presented as a particularly suited form for the time-frequency analysis of transients and other non-stationary phenomena. Its effectiveness is illustrated byapplying it to the problem of electron density profile measurement through broadband microwave reflectometry in fusiondevices, its advantages being demonstrated via a detailed comparison with the well known short time Fourier transformspectrogram. In particular, the Wigner distribution is used in a novel application as a means not only to retrievefrom reflectometry data the instantaneous frequency needed for profile inversion, but also to provide an accuraterepresentation of reflectometry signals in the time-frequency plane. Further, in a careful discussion stressing itsbenefits relative to more standard approaches based on the quadrature signal, the analyticsignal is proposed as being appropriate to routinely extract from reflectometry data anunambiguously defined set of instantaneous amplitude, phase and frequency. The problemsassociated with the fact that digitized reflectometry data give rise to discrete time signals areproperly handled, and the different estimates for the instantaneous frequency obtained from the Wignerdistribution and the spectrogram by calculating their first frequency moments and mean frequencies,as well as by locating their peaks, are also compared.