Bujack, E. H., G. Scheuermann, Demystification of the Geometric Fourier Transforms and resulting Convolution Theorems, Mathematical Methods in the Applied Sciences, Article first published online: 3 Sep. 2015. DOI: 10.1002/mma.3607.
Abstract: As it will turn out in this paper, the recent hype about most of the Clifford–Fourier transforms is not thoroughly worth the pain. Almost everyone that has a real application is separable, and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial.
Keywords: geometric algebra; Clifford algebra; Fourier transform; trigonometric transform; convolution theorem