Affiliation:
1. Department for Biophysics, Neuroscience and Biomedical Engineering, Center for Multidisciplinary Studies, University of Belgrade, Despot Stefan Boulevard 142, 11000 Belgrade, Serbia and Montenegro
2. Institute for Biological Research "Sinisa Stankovic", Despot Stefan Boulevard 142, Belgrade, Serbia and Montenegro
Abstract
We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients [Formula: see text], mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of [Formula: see text], n = 2,3,…,n max , exhibited linear dependence on n: [Formula: see text] with stable slopes and Y-intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y-intercepts and signal fractal dimension: [Formula: see text] and calculated parameters A(n max ) and B(n max ) for n max = 3,…,7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k max , since the smallest error was obtained with n max = 3.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modelling and Simulation
Reference9 articles.
1. Approach to an irregular time series on the basis of the fractal theory
2. J. Virkala, Simplicity Behind Complexity, ed. W. Klonowski (Pabst Science Publish, Lengerich, 2004) pp. 367–376.
Cited by
21 articles.
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