## New Developments in Clifford Fourier Transforms

**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.

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### Submission history

[v1] 2014-07-21 15:55:09

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