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Wavelet Based Approach to Fractals and Fractal Signal Denoising

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Transactions on Computational Science VI

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5730))

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Abstract

In this paper localized fractals are studied by using harmonic wavelets. It will be shown that, harmonic wavelets are orthogonal to the Fourier basis. Starting from this, a method is defined for the decomposition of a suitable signal into the periodic and localized parts. For a given signal, the denoising will be done by simply performing a projection into the wavelet space of approximation. It is also shown that due to their self similarity property, a good approximation of fractals can be obtained by a very few instances of the wavelet series. Moreover, the reconstruction is independent on scale as it should be according to the scale invariance of fractals.

Preliminary results presented at the International Conference on Computational Science and Applications (ICCSA 2008), June 30-July 3, 2008 Perugia (It) .

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Author information

Authors and Affiliations

  1. DiFarma, University of Salerno, Via Ponte Don Melillo, I-84084, Fisciano, (SA)

    Carlo Cattani

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  1. Carlo Cattani
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

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Cattani, C. (2009). Wavelet Based Approach to Fractals and Fractal Signal Denoising . In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science VI. Lecture Notes in Computer Science, vol 5730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10649-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-10649-1_9

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