八元数分数阶傅里叶变换的微分性质研究  

A Study on the Differential Properties of Fractional Fourier Transforms of Octonions

作　　者：杨茜 冯强[1] 蒋楠 姬锦仪 YANG Xi;FENG Qiang;JIANG Nan;JI Jinyi(School of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州大学学报(自然科学版)》2025年第1期7-11,41,共6页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(62261055,61861044);陕西省自然科学基金资助项目(2022JM-400,2023-JC-YB-085);延安大学研究生教育创新资助项目(YCX2024043);陕西省大学生创新创业训练计划资助项目(202410719039)。

摘　　要：八元数分数阶傅里叶变换作为一种新颖的信号处理工具,在处理复杂信号和多维数据方面具有潜力。本文针对八元数分数阶傅里叶变换的偏微分性质展开研究。首先介绍了八元数及其四元数分数阶傅里叶变换的基本概念和数学表达式,在此基础上定义了八元数分数阶傅里叶变换;其次在详细分析了八元数分数阶傅里叶变换的基础上,通过数学证明,给出了八元数分数阶傅里叶变换多种形式的微分性质。本文的研究可以为八元数分数阶傅里叶变换在信号处理领域的进一步应用提供理论与方法支撑。The octonion fractional Fourier transform,as a novel signal processing tool,has great potential in processing complex signals and multi-dimensional data.This paper studies the partial differential properties of octonion fractional Fourier transforms.First,it introduces the basic concept and mathematical expression of octonion and quaternion fractional Fourier transform,thus the fractional Fourier transform of octonion is defined.Then,based on a detailed analysis fractional Fourier transform,it provides mathematical proofs for the differential properties of various forms of octonion fractional Fourier transform.The research provides both theoretical and methodological support for further applications of the octonion fractional Fourier transform in the field of signal processing.

关 键 词：分数阶傅里叶变换 八元代数 微分性质 

分 类 号：O174.2[理学—数学]