Wavelet analysis as a nonstationary plasma fluctuation diagnostic tool

Summary form only given. Analysis of nonstationary plasma fluctuation data has been a long-time challenge for the plasma diagnostic community. Many fluctuation diagnostic tools are Fourier-based such as power spectra and S(k,/spl omega/), to mention just a few. These diagnostic tools are particularly useful in analyzing stationary plasma fluctuation data. However, they have limited utility, if any at all, when the fluctuations are statistically nonstationary. For this reason, in this paper we present and apply wavelet transforms as a new diagnostic tool to analyze nonstationary plasma fluctuation data. Unlike the Fourier transform, which represents a given signal globally without temporal resolution, the wavelet transform provides local representation of the given signal in the time-scale domain. Compared to the so-called short-time Fourier transform, the wavelet transform has multiresolution capabilities. These capabilities enable the wavelet transform to analyze a given nonstationary signal at various time-scale resolutions. The fundamental concepts and multiresolution properties of wavelet transforms, along with a brief comparison with the short-time Fourier transform, are presented in this paper. The selection of a prototype wavelet or a mother wavelet is also discussed. The efficacy of the wavelet approach is demonstrated by analyzing transient broadband electrostatic potential fluctuations inside the inversion radius of sawtoothing TEXT-U plasmas during electron cyclotron resonance heating.