Empirical Mode Decomposition and its Application to Palm Tree Mode Analysis

Fourier Transformation is one of the workhorses in time series analysis. If nonlinear effects deform the wave profiles of measured data, FFT needs additional harmonic components to simulate these profiles. Non-stationarity and nonlinearity therefore induce spurious harmonic components. These short-comings can also be found in wavelet analysis if the popular Morlet wavelet is used since it is Fourier based. In order to overcome these problems, the adaptive time-frequency data analysis method "Empirical Mode Decomposition" (EMD) is suitable. EMD acts as a dyadic filter bank to decompose the series into a finite set of so-called Intrinsic Mode Functions (IMF). Each IMF reflect the data on a different time-scale and admit well-behaved Hilbert transforms.With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. We applied EMD on MHD and ECE "Palm Tree Mode" (PTM) data. Hilbert amplitude spectra of data from the fast poloidal coil arrays show that the PTM is a coherent structure. The results prove in an independent way that the higher harmonics as seen in the FFT are a consequence of the high localization of the PTM structure. The effect of the mode on the temperature measured by ECE is twofold. One is the increase in temperature measured as temperature inside the filament. The other is the change in temperature perceived through the change in geometry by the magnetic perturbation of the PTM. These two contributions have been separated for the first time. EMD from a single signal thereby consistently supports the assumption that the PTM is indeed a current filament. Comparisons between FFT, wavelet analysis and EMD will be presented to highlight strengths and weaknesses of the individual methods.
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