The understanding of turbulence in magnetized plasmas and its role in the cross field transport is still greatly incomplete. Several previous works reported on evidences of long-time correlations compatible with an avalanche-type of radial transport. Persistence properties in time records have been deduced from high values of the Hurst exponent obtained with the rescaled range R∕S analysis applied to experimental probe data acquired in the edge of tokamaks. In this paper the limitations of this R∕S method, in particular when applied to signals having mixed statistics are investigated, and the great advantages of the wavelets decomposition as a tool to characterize the self-similarity properties of experimental signals are highlighted. Furthermore the analysis of modified simulated fractional Brownian motions (fBm) and fractional Gaussian noises (fGn) allows us to discuss the relationship between high values of the Hurst exponent and long range correlations. It is shown that for such simulated signals with mixed statistics persistence at large time scales can still reflect the self-similarity properties of the original fBm and do not imply the existence of long range correlations, which are destroyed. It is thus questionable to assert the existence of long range correlations for experimental signals with non-Gaussian and mixed statistics just from high values of the Hurst exponent.
International audienceThe purpose of this communication is to show that wavelet transform provides a relevant way to the Fourier transform in the case of central frequency measurement of a SAW resonator. After recalling the limits of the Fourier transform, we present a method based on wavelet transform modulus maxima which allows staying in the time domain without using the frequency domain. We show that this approach is a way to improve the spectral resolution and we propose a technique, checked on experimental signals, able to measure the SAW resonator frequency according to the desired spectral resolution
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