holder

Purpose

Hölder exponent estimation through an affine TFR.

Synopsis

h = holder(tfr,f)
h = holder(tfr,f,n1)
h = holder(tfr,f,n1,n2)
h = holder(tfr,f,n1,n2,t)

Description

holder estimates the Hölder exponent of a signal through an affine time-frequency representation of it.

Name	Description	Default value
tfr	affine time-frequency representation
f	frequency values of the spectral analysis
n1	indice of the minimum frequency for the linear regression	1
n2	indice of the maximum frequency for the linear regression	length(f)
t	time vector. If t is omitted, the function returns the global estimate of the Hölder exponent. Otherwise, it returns the local estimates h(t) at the instants specified in t
h	output value (if t omitted) or vector (otherwise) containing the Hölder estimate(s)

Example

For instance, we consider a 64-points Lipschitz singularity (see anasing) of strength h=0, centered at t0=32, analyze it with the scalogram (Morlet wavelet with half-length = 4), and estimate its Hölder exponent,

         sig=anasing(64);
         [tfr,t,f]=tfrscalo(sig,1:64,4,0.01,0.5,256,1);
         h=holder(tfr,f,1,256,1:64);

the value obtained at time t0 is a good estimation of h (we obtain h(t0)=-0.0381).

See Also

anastep, anapulse, anabpsk, doppler.

Reference

[1] S. Jaffard ``Exposants de Hölder en des points donnés et coefficients d'ondelettes'' C.R. de l'Académie des Sciences, Paris, t. 308, Série I, p. 79-81, 1989.

[2] P. Gonçalvès, P. Flandrin ``Scaling Exponents Estimation From Time-Scale Energy Distributions'' IEEE ICASSP-92, pp. V.157 - V.160, San Fransisco 1992.

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