Fractional Fourier transform on ℝ2 and an application

被引:0
|
作者
Yue Zhang
Wenjuan Li
机构
[1] Northwestern Polytechnical University,School of Mathematics and Statistics
来源
Frontiers of Mathematics | 2022年 / 17卷
关键词
Fractional Fourier transform (FRFT); inverse fractional Fourier transform; signal recovery; direct sum decomposition; general Heisenberg inequality; 42B10; 65D30;
D O I
暂无
中图分类号
学科分类号
摘要
We focus on the Lp (ℝ2) theory of the fractional Fourier transform (FRFT) for 1 ⩽ p ⩽ 2. In L1 (ℝ2), we mainly study the properties of the FRFT via introducing the two-parameter chirp operator. In order to get the pointwise convergence for the inverse FRFT, we introduce the fractional convolution and establish the corresponding approximate identities. Then the well-defined inverse FRFT is given via approximation by suitable means, such as fractional Gauss means and Able means. Furthermore, if the signal ℱα,βf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal F}_{\alpha ,\beta }}f$$\end{document} is received, we give the process of recovering the original signal f with MATLAB. In L2 (ℝ2), the general Plancherel theorem, direct sum decomposition, and the general Heisenberg inequality for the FRFT are obtained.
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页码:1181 / 1200
页数:19
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