E.M.S. Hitzer
Quaternion Fourier Transform on Quaternion Fields and Generalizations
in S.L. Eriksson, R.S. Krausshar (eds.), Proc. of Function Theories in Higher Dimensions, Tampere 2006, Advances in Applied Clifford Algebras, 17(3), pp. 497-517 (2007).

Abstract: We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.

Mathematics Subject Classification (2000). Primary 42A38; Secondary 11R52.

Keywords. Quaternions, Fourier transform, Clifford algebra, volume-time al- gebra, spacetime algebra, automorphisms.

The original publication with DOI 10.1007/s00006-007-0037-8 is available at www.springerlink.com.

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