分数阶 Fourier 变换的测不准原理

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 257-264.

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分数阶 Fourier 变换的测不准原理

周悦(),杨燕^*()

中山大学数学学院(珠海) 广东珠海 519082

收稿日期:2022-09-05 修回日期:2023-02-14 出版日期:2024-04-26 发布日期:2024-04-07
通讯作者: * 杨燕, Email:yangyan8@mail.sysu.edu.cn
作者简介:周悦,Email:zhouy583@mail2.sysu.edu.cn

Uncertainty Principles of Fractional Fourier Transform

Zhou Yue(),Yang Yan^*()

School of Mathematics (Zhuhai), Sun Yat-Sen University, Guangdong Zhuhai 519082

Received:2022-09-05 Revised:2023-02-14 Online:2024-04-26 Published:2024-04-07

摘要/Abstract

摘要：

该文参考 Fourier 变换的性质研究了离散分数阶 Fourier 变换的测不准原理以及连续分数阶 Fourier 变换在 Lebesgue 测度下的测不准原理, 使得分数阶 Fourier 变换的测不准原理性质更一般化.

关键词: 连续分数阶 Fourier 变换, 离散分数阶 Fourier 变换, 测不准原理

Abstract:

Referring to the properties of Fourier transform, the authors find the uncertainty principle of discrete fractional Fourier transform and uncertainty principle of continuous fractional Fourier transform under Lebesgue measure, which makes the uncertainty principles of fractional Fourier transform more general.

Key words: Continuous fractional Fourier transform, Discrete fractional Fourier transform, Uncertainty principle

中图分类号:

O177.92

周悦, 杨燕. 分数阶 Fourier 变换的测不准原理[J]. 数学物理学报, 2024, 44(2): 257-264.

Zhou Yue, Yang Yan. Uncertainty Principles of Fractional Fourier Transform[J]. Acta mathematica scientia,Series A, 2024, 44(2): 257-264.

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参考文献 8

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[6]	Shi J, Han M, Zhang N. Uncertainty principles for discrete signals associated with the fractional Fourier and linear canonical transforms. Signal Image Video P, 2016, 10(8): 1519-1525
[7]	Zayed A I. On the relationship between the Fourier and fractional Fourier transforms. IEEE Signal Proc Let, 1996, 3(12): 310-311 doi: 10.1109/97.544785
[8]	Halmos P R, Sunder V S. Bounded Integral Operators on L2 Spaces. Berlin: Springer-Verlag, 1978

分数阶 Fourier 变换的测不准原理

Uncertainty Principles of Fractional Fourier Transform

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