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arXiv · 1603.05471

Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

Diederik Aerts·Marek Czachor·Maciej Kuna
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Abstract

Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the expected basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

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BibTeXRIS

Diederik Aerts, Marek Czachor, Maciej Kuna. 2016-03-17. Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus. https://doi.org/10.1016/j.chaos.2016.07.008

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