Quaternion Fourier Transform on Quaternion Fields and Generalizations
Rings and Algebras
2013-06-06 v1 Computer Vision and Pattern Recognition
Mathematical Physics
math.MP
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 () 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.
Cite
@article{arxiv.1306.1023,
title = {Quaternion Fourier Transform on Quaternion Fields and Generalizations},
author = {Eckhard Hitzer},
journal= {arXiv preprint arXiv:1306.1023},
year = {2013}
}
Comments
21 pages