Chapter

Transactions on Computational Science VI

Volume 5730 of the series Lecture Notes in Computer Science pp 143-162

Wavelet Based Approach to Fractals and Fractal Signal Denoising

  • Carlo CattaniAffiliated withLancaster UniversityDiFarma, University of Salerno

* Final gross prices may vary according to local VAT.

Get Access

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.

Keywords

Harmonic Wavelets Weierstrass Function Scale Invariance Fractals Denoising