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

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 by applying it to the problem of electron density profile measurement through broadband microwave reflectometry in fusion devices, its advantages being demonstrated via a detailed comparison with the well known short time Fourier transform spectrogram. In particular, the Wigner distribution is used in a novel application as a means not only to retrieve from reflectometry data the instantaneous frequency needed for profile inversion, but also to provide an accurate representation of reflectometry signals in the time-frequency plane. Further, in a careful discussion stressing its benefits relative to more standard approaches based on the quadrature signal, the analytic signal is proposed as being appropriate to routinely extract from reflectometry data an unambiguously defined set of instantaneous amplitude, phase and frequency. The problems associated with the fact that digitized reflectometry data give rise to discrete time signals are properly handled, and the different estimates for the instantaneous frequency obtained from the Wigner distribution and the spectrogram by calculating their first frequency moments and mean frequencies, as well as by locating their peaks, are also compared.