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arXiv · 1306.2184

A General Geometric Fourier Transform

Roxana Bujack·Gerik Scheuermann·Eckhard Hitzer
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Abstract

The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature. We show which constraints are additionally necessary to obtain certain features like linearity or a shift theorem. As a result, we provide guidelines for the target-oriented design of yet unconsidered transforms that fulfill requirements in a specific application context. Furthermore, the standard theorems do not need to be shown in a slightly different form every time a new geometric Fourier transform is developed since they are proved here once and for all.

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Roxana Bujack, Gerik Scheuermann, Eckhard Hitzer. 2013-06-10. A General Geometric Fourier Transform. https://arxiv.org/abs/1306.2184

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