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IEEE SIGNAL PROCESSING MAGAZINE [38] JULY 2007 1053-5888/07/$25.002007IEEE ultifractal analysis is becoming a standard statistical analysis technique. In
 

Summary: IEEE SIGNAL PROCESSING MAGAZINE [38] JULY 2007 1053-5888/07/$25.00©2007IEEE
M
ultifractal analysis is becoming a standard statistical analysis technique. In
signal processing, it mostly consists of estimating scaling exponents charac-
terizing scale invariance properties. For practical purposes, confidence inter-
vals in estimation and p values in hypothesis testing are of primary
importance. In empirical multifractal analysis, the statistical performance of
estimation or test procedures remain beyond analytical derivation because of the theoretically
involved nature of multifractal processes. Therefore, the goal of this article is to show how non-
parametric bootstrap approaches circumvent such limitations and yield procedures that exhibit
satisfactory statistical performance and can hence be practically used on real-life data. Such
tools are illustrated at work on the analysis of the multifractal properties of empirical hydrody-
namic turbulence data.
MOTIVATION: BOOTSTRAP FOR MULTIFRACTAL ANALYSIS?
SCALE INVARIANCE
The concept of scale invariance, or scaling, refers to systems or signals for which no scale of time
or space can be identified as playing a characteristic role. Historically, scale invariance had been
tied to 1/f spectrum for stochastic second-order stationary processes. However, it has been
shown [1] that scale invariance can fruitfully be modeled with self-similar [2] and/or multifractal
[Herwig Wendt, Patrice Abry, and Stéphane Jaffard

  

Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon

 

Collections: Engineering