1. Overview

This area of Fraclab is dedicated to the estimation of various exponents that arise constantly in the (multi)fractal analysis of signals. These are :

• The pointwise Hölder exponent, which characterizes the regularity of the measure/function under consideration at any given point.
• The local Hölder exponent, which is related to the regularity of the measure/function under consideration around any given point.
• The (abusively called) long range dependence exponent ; this one describes the (possible) power law behaviour of the Fourier power spectrum at frequencies close to 0.
• The four parameters of a stable motion : see the Synthesis pop-up menu help for a brief description of stable motions.
• The 2-microlocal exponents : these yield a finer description of the local regularity properties of a signal, which goes beyond the Hölder exponents.

Pointwise and local exponents, as well as 2-microlocal exponents, are defined at each point. Thus, when we talk of estimating one of these exponents, we really mean estimating them at all points, i.e. estimating e.g. a pointwise exponents function. In other words, the output is a new signal, rather than a number, as is the case when we compute the LRD exponent.