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   -> Volume 5, Issue 5

Preprint: Wavelet Packet Computation of the Hurst Exponent
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Cameron Jones (

PostPosted: Wed Dec 04, 2002 9:53 am    
Subject: Preprint: Wavelet Packet Computation of the Hurst Exponent
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Preprint: Wavelet Packet Computation of the Hurst Exponent

Article: Wavelet Packet Computation of the Hurst Exponent
Cameron L. Jones, Greg T. Lonergan and David E. Mainwaring

Centre for Applied Colloid and BioColloid Science, School of
Chemical Sciences, Swinburne University of Technology, Hawthorn 3122,

Department of Applied Chemistry, Royal Melbourne Institute of Technology,
Melbourne 3001, Australia

ABSTRACT: Wavelet Packet Analysis was used to measure the global
scaling behaviour of homogeneous fractal signals from the slope of
decay for discrete wavelet coefficients belonging to the adapted
wavelet best basis. A new scaling function for the size distribution
correlation between wavelet coefficient energy magnitude and position
in a sorted vector listing is described in terms of a power law to
estimate the Hurst exponent. Profile irregularity and long-range
correlations in self-affine systems can be identified and indexed with
the Hurst exponent, and synthetic one-dimensional fractional Brownian
motion (fBm) type profiles are used to illustrate and test the
proposed wavelet packet expansion. We also demonstrate an initial
application to a biological problem concerning the spatial
distribution of local enzyme concentration in fungal colonies which
can be modelled as a self-affine trace or an 'Enzyme Walk'. The
robustness of the wavelet approach applied to this stochastic system
is presented, and comparison is made between the wavelet packet method
and the root-mean-square roughness and second-moment approaches for
both examples. The wavelet packet method to estimate the global Hurst
exponent appears to have similar accuracy compared with other methods,
but its main advantage is the extensive choice of available analyzing
wavelet filter functions for characterizing periodic and oscillatory

# To whom correspondence should be addressed. Email:

Additional information: This wavelet packet method was performed using
Wavelet Packet Laboratory for Windows developed by Ronald Coifman, Kresimir
Ukraincik, and Victor Wickerhauser (A.K. Peters Ltd., 1993). A method for
applying wavelet packets to estimate multifractal scaling in 1-D signals is
also presented. The method is demonstated on a biological problem.

Reference: Jones, C.L., Lonergan, G.T. and Mainwaring, D.E. (1996). Wavelet
Packet Computation of the Hurst Exponent. Journal of Physics A: Mathematical
and General. 29:2509-2527.

Cameron L. Jones (Research Fellow)
Centre for Applied Colloid and BioColloid Science Swinburne University
of Technology School of Chemical Sciences P.O. Box 218 Hawthorn=20
Victoria, 3122 AUSTRALIA

Tel: +613 9214 8935 Fax: +613 9819 0834 Email:
All times are GMT + 1 Hour
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