Quaternion Fourier Transform on Quaternion Fields and Generalizations
Author: Hitzer, Eckhard
Source: Advances in Applied Clifford Algebras, Volume 17, Number 3, August 2007 , pp. 497-517(21)
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.
Document Type: Research Article
Affiliations: Email: email@example.com
Publication date: 2007-08-01