Special Affine Fourier Transform for Space-Time Algebra Signals in Detail

被引：0
作者：
Eckhard Hitzer
机构：
[1] International Christian University,
来源：
Advances in Applied Clifford Algebras | 2022年 / 32卷
关键词：
Clifford’s geometric algebra; Space-time; Space-time algebra; Special affine Fourier transform; Uncertainty principle;
D O I：
暂无
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学科分类号：
摘要：
We generalize the space-time Fourier transform (SFT) (Hitzer in Adv Appl Clifford Algebras 17(3):497–517, 2007) to a special affine Fourier transform (SASFT, also known as offset linear canonical transform) for 16-dimensional space-time multivector Cl(3, 1)-valued signals over the domain of space-time (Minkowski space) R3,1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{3,1}.$$\end{document} We establish how it can be computed in terms of the SFT, and introduce its properties of multivector coefficient linearity, shift and modulation, inversion, Rayleigh (Parseval) energy theorem, partial derivative identities, a directional uncertainty principle and its specialization to coordinates. All important results are proven in full detail.
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