A General Geometric Fourier Transform
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.
Cite
@article{arxiv.1306.2184,
title = {A General Geometric Fourier Transform},
author = {Roxana Bujack and Gerik Scheuermann and Eckhard Hitzer},
journal= {arXiv preprint arXiv:1306.2184},
year = {2013}
}
Comments
First presented in Proc. of The 9th Int. Conf. on Clifford Algebras and their Applications, (2011)