New Convolution Related Theorems and Applications Associated with Offset Linear Canonical Transform

被引：0
作者：
Mahato, Gita Rani [1 ]
Varghese, Sarga [1 ]
Kundu, Manab [1 ]
机构：
[1] SRM Univ AP, Dept Math, Amaravati 522240, India
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2025年 / 19卷 / 05期
关键词：
Fourier transform; Offset linear canonical transform; Convolution; Correlation; PALEY-WIENER THEOREMS; FRACTIONAL FOURIER; BOAS THEOREMS; PRODUCT; EIGENFUNCTIONS;
D O I：
10.1007/s11785-025-01739-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we define new type of convolution and correlation theorems associated with the offset linear canonical transform (OLCT). Additionally, we discuss their applications in multiplicative filter design, which may prove useful in optics and signal processing for signal recovery. Furthermore, we explore the real Paley-Wiener (PW) and Boas theorems for the OLCT, analyzing signal characteristics for OLCT within the L2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2(\mathbb {R})$$\end{document} domain.
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页数：18
相关论文
共 36 条
[1]   OPTICAL OPERATIONS ON WAVE-FUNCTIONS AS THE ABELIAN SUBGROUPS OF THE SPECIAL AFFINE FOURIER TRANSFORMATION [J].
ABE, S ;
SHERIDAN, JT .
OPTICS LETTERS, 1994, 19 (22) :1801-1803
[2]  
Ahmad O., 2024, Wigner-Ville Distribution Associated with the Biquaternion Offset Linear Canonical Transform
[3]   Product and convolution theorems for the fractional Fourier transform [J].
Almeida, LB .
IEEE SIGNAL PROCESSING LETTERS, 1997, 4 (01) :15-17
[4]   Real Paley-Wiener theorems for Fourier series [J].
Andersen, Nils Byrial .
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (10) :3815-3829
[5]   REAL PALEY-WIENER THEOREMS AND LOCAL SPECTRAL RADIUS FORMULAS [J].
Andersen, Nils Byrial ;
de Jeu, Marcel .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (07) :3613-3640
[6]   Two New Convolutions for the Fractional Fourier Transform [J].
Anh, P. K. ;
Castro, L. P. ;
Thao, P. T. ;
Tuan, N. M. .
WIRELESS PERSONAL COMMUNICATIONS, 2017, 92 (02) :623-637
[7]   A PROPERTY OF INFINITELY DIFFERENTIABLE FUNCTIONS [J].
BANG, HH .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 108 (01) :73-76
[8]   Scaled Wigner distribution in the offset linear canonical domain [J].
Bhat, M. Younus ;
Dar, Aamir H. .
OPTIK, 2022, 266
[9]   Convolution and correlation theorems for Wigner-Ville distribution associated with the quaternion offset linear canonical transform Convolution and correlation theorems for WVD associated with the QOLCT [J].
Bhat, M. Younus ;
Dar, Aamir H. .
SIGNAL IMAGE AND VIDEO PROCESSING, 2022, 16 (05) :1235-1242
[10]   Convolution theorems for the linear canonical transform and their applications [J].
Deng Bing ;
Tao Ran ;
Wang Yue .
SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES, 2006, 49 (05) :592-603
1234