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Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2017

Finite-Resolution Effects in $p$ -Leader Multifractal Analysis

Résumé

Multifractal analysis has become a standard signal processing tool,for which a promising new formulation, the p-leader multifractal formalism, has recently been proposed. It relies on novel multiscale quantities, the p-leaders, defined as local l^p norms of sets of wavelet coefficients located at infinitely many fine scales. Computing such infinite sums from actual finite-resolution data requires truncations to the finest available scale, which results in biased p-leaders and thus in inaccurate estimates of multifractal properties. A systematic study of such finite-resolution effects leads to conjecture an explicit and universal closed-form correction that permits an accurate estimation of scaling exponents. This conjecture is formulated from the theoretical study of a particular class of models for multifractal processes, the wavelet-based cascades. The relevance and generality of the proposed conjecture is assessed by numerical simulations conducted over a large variety of multifractal processes. Finally, the relevance of the proposed corrected estimators is demonstrated on the analysis of heart rate variability data.

Dates et versions

hal-01620209 , version 1 (20-10-2017)

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Citer

Roberto Leonarduzzi, Herwig Wendt, Patrice Abry, Stéphane Jaffard, Clothilde Melot. Finite-Resolution Effects in $p$ -Leader Multifractal Analysis. IEEE Transactions on Signal Processing, 2017, 65 (13), pp.3359 - 3368. ⟨10.1109/TSP.2017.2690391⟩. ⟨hal-01620209⟩
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