GRIVEL, Eric; BERTHELOT, Bastien; LEGRAND, Pierrick

doi:10.1016/j.dsp.2021.103346

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GRIVEL, Eric
Laboratoire de l'intégration, du matériau au système [IMS]

BERTHELOT, Bastien
THALES Avionics Electrical Systems [TAES]
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]

LEGRAND, Pierrick
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
Institut de Mathématiques de Bordeaux [IMB]
Université de Bordeaux [UB]

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Digital Signal Processing. 2021

Elsevier

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The fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.< Leer menos

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DFA

Statistical analysis

Variance

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A matrix approach to get the variance of the square of the fluctuation function of the DFA

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