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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.
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