Quaternion fourier transform on quaternion fields and generalizations

被引：215

作者：

Hitzer, Eckhard M. S. ^{[1
]}

机构：

[1] Univ Fukui, Dept Appl Phys, 3-9-1 Bunkyo, Fukui 9108507, Japan

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2007年 / 17卷 / 03期

关键词：

Quaternions; Fourier transform; Clifford algebra; volume-time algebra; spacetime algebra; automorphisms;

D O I：

10.1007/s00006-007-0037-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：497 / 517

页数：21

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