An uncertainty principle for quaternion Fourier transform

被引：121

作者：

Bahri, Mawardi ^{[2
]}

Hitzer, Eckhard S. M. ^{[2
]}

Hayashi, Akihisa ^{[2
]}

Ashino, Ryuichi ^{[1
]}

机构：

[1] Osaka Kyoiku Univ, Div Math Sci, Osaka 5828582, Japan

[2] Univ Fukui, Dept Appl Phys, Fukui 9108507, Japan

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 56卷 / 09期

关键词：

Quaternion algebra; Quaternionic Fourier transform; Uncertainty principle; Gaussian quaternion signal; Hypercomplex functions;

D O I：

10.1016/j.camwa.2008.05.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2398 / 2410

页数：13

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