Authors: Eckhard Hitzer
We show how real and complex Fourier transforms are extended to W.R. Hamilton's algebra of quaternions and to W.K. Clifford’s geometric algebras. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Clifford's geometric algebras are complete algebras, algebraically encoding a vector space and all its subspace elements. Applications include electromagnetism, and the processing of images, color images, vector field and climate data. Further developments of Clifford Fourier Transforms include operator exponential representations, and extensions to wider classes of integral transforms, like Clifford algebra versions of linear canonical transforms and wavelets.
Comments: 7 Pages. in N. E. Mastorakis, P. M. Pardalos, R. P. Agarwal, L. Kocinac (eds.), Adv. in Appl. and Pure Math., Proc. of the 2014 Int. Conf. on Pure Math., Appl. Math., Comp. Methods (PMAMCM 2014), Santorini, Greece, July 2014, Math. & Comp. in Sci. & Eng., Vol. 29.
[v1] 2014-07-21 15:55:09
Unique-IP document downloads: 155 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.