Quaternion Fourier Transform on Quaternion Fields and Generalizations
E. Hitzer, Department of Applied Physics, University of Fukui, 3-9-1 Bunkyo, 910-8507 Fukui, Japan
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 algebra – spacetime algebra – automorphisms
I thank my family and FTHD organizer S.L. Eriksson.
Soli Deo Gloria
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