Determination of the Hurst exponent by use of wavelet transforms
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In this article, a method for global Hurst exponent determination based on wavelets was proposed, and the results were compared to those obtained with Fourier spectral analysis when many samples are available.Abstract:
We propose a method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces, and data from economy. The results are compared to those obtained with Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin.read more
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References
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Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
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Fractal Geometry: Mathematical Foundations and Applications
TL;DR: In this article, a mathematical background of Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractality products of fractal intersections of fractalities.
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Scaling Phenomena in Disordered Systems
Roger Pynn,Arne T. Skjeltorp +1 more
TL;DR: In this article, the scaling properties of random fractuals were studied in the context of particle aggregation and scaling in a model of Cement Gels, and the results showed that the scaling of a model can be described as a function of the number of particles in the model.