5 research outputs found
A General Geometric Fourier Transform
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.Comment: First presented in Proc. of The 9th Int. Conf. on Clifford Algebras
and their Applications, (2011