Section: New Results

Interpréter les Fonctions de Fluctuation du DFA et du DMA comme le Résultat d'un Filtrage

Abstract : The detrended uctuation analysis (DFA) and the detrending moving average (DMA) are often used to estimate the regularity of the signal, since they do not require a strong expertise in the eld of signal processing while providing good results. In this paper, our contribution is twofold. We propose a framework that allows these approaches to be compared. It is based on a matrix form of the square of the uctuation function. Using the above representation for wide-sense-stationary processes, we show that the statistical mean of the square of the uctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The dierences between both methods can be highlighted. It also conrms that they can be seen as ad hoc wavelet based techniques to estimate the Hurst exponent.

Authors : Bastien Berthelot, Eric Grivel, Pierrick Legrand, Jean-Marc Andre, Patrick Mazoyer, et al.