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Problems of Estimating Fractal Dimension by Higuchi and DFA Methods for Signals That Are a Combination of Fractal and Oscillations

May 2021

DOI:10.23919/Measurement52780.2021.9446804

Conference: 2021 13th International Conference on Measurement

Authors:

Slovak Academy of Sciences

Stochastic fractals of the 1/f noise type are an important manifestation of the brain’s electrical activity and other real-world complex systems. Fractal complexity can be successfully estimated by methods such as the Higuchi method and detrended fluctuation analysis (DFA). In this study, we show that if, as with the EEG, the signal is a combination of fractal and oscillation, the estimates of fractal characteristics will be inaccurate. On our test data, DFA overestimated the fractal dimension, while the Higuchi method led to underestimation in the presence of high-amplitude, densely sampled oscillations.

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Article

Approach to an irregular time series on the basis of the fractal theory

Article

Jun 1988
PHYSICA D

T. Higuchi

We present a technique to measure the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval. First we apply it to a fractional Brownian function [1] which has a property of self-similarity for all scales, and we can get the stable and precise fractal dimension. This technique is also applied to the observational data of natural phenomena. It does not show self-similarity all over the scale but has a different self-similarity across the characteristic time scale. The present method gives us a stable characteristic time scale as well as the fractal dimension.