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Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms 基于四元数傅里叶变换和线性正则变换的二维四元数信号采样定理
Hu, Xiaoxiao1; Cheng, Dong2; Kou, Kit Ian3
2022-03-01
Source PublicationFrontiers of Information Technology and Electronic Engineering
ISSN2095-9184
Volume23Issue:3Pages:463-478
Abstract

The main purpose of this paper is to study different types of sampling formulas of quaternionic functions, which are bandlimited under various quaternion Fourier and linear canonical transforms. We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms. In addition, the relationships among different types of sampling formulas under various transforms are discussed. First, if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin, then the sampling formulas under various quaternion Fourier transforms are identical. If this rectangle is not symmetric about the origin, then the sampling formulas under various quaternion Fourier transforms are different from each other. Second, using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform, we derive sampling formulas under various quaternion linear canonical transforms. Third, truncation errors of these sampling formulas are estimated. Finally, some simulations are provided to show how the sampling formulas can be used in applications.

KeywordGeneralized Quaternion Partial And Total Hilbert Transforms O236 Quaternion Fourier Transforms Quaternion Linear Canonical Transforms Quaternion Partial And Total Hilbert Transforms Sampling Theorem Truncation Errors
DOI10.1631/FITEE.2000499
URLView the original
Indexed BySCIE
Language中文Chinese
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Computer Science, Software Engineering ; Engineering, Electrical & Electronic
WOS IDWOS:000773924300009
Scopus ID2-s2.0-85127253269
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorHu, Xiaoxiao
Affiliation1.The First Affiliated Hospital of Wenzhou Medical University, Wenzhou Medical University, Wenzhou, 325000, China
2.Research Center for Mathematics and Mathematics Education, Beijing Normal University (Zhuhai), Zhuhai, 519087, China
3.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao
Recommended Citation
GB/T 7714
Hu, Xiaoxiao,Cheng, Dong,Kou, Kit Ian. Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms 基于四元数傅里叶变换和线性正则变换的二维四元数信号采样定理[J]. Frontiers of Information Technology and Electronic Engineering,2022,23(3):463-478.
APA Hu, Xiaoxiao,Cheng, Dong,&Kou, Kit Ian.(2022).Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms 基于四元数傅里叶变换和线性正则变换的二维四元数信号采样定理.Frontiers of Information Technology and Electronic Engineering,23(3),463-478.
MLA Hu, Xiaoxiao,et al."Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms 基于四元数傅里叶变换和线性正则变换的二维四元数信号采样定理".Frontiers of Information Technology and Electronic Engineering 23.3(2022):463-478.
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