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Generalized sampling expansions associated with quaternion Fourier transform
Cheng, Dong; Kou, Kit Ian
2018-07-30
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Volume41Issue:11Pages:4021-4032
Abstract

Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion-valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a sigma-bandlimited quaternion-valued signal in QFT sense can be reconstructed from the samples of output signals of M linear systems based on QFT. Quaternion linear canonical transform is a generalization of QFT with six parameters. Using the relationship between QFT, we derive the sampling formula for sigma-bandlimited quaternion-valued signal in quaternion linear canonical transform sense. Examples are given to illustrate our results. Copyright (c) 2017 John Wiley & Sons, Ltd.

KeywordQuaternion-valued Signals Quaternion Fourier Transform Quaternion Linear Canonical Transform Generalized Sampling Expansions Generalized Translation Convolution Theorem
DOIhttps://doi.org/10.1002/mma.4423
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000435802000002
PublisherWILEY
The Source to ArticleWOS
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorKou, Kit Ian
AffiliationDepartment of Mathematics, Faculty of Science and Technology, University of Macau, Macau
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Cheng, Dong,Kou, Kit Ian. Generalized sampling expansions associated with quaternion Fourier transform[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2018,41(11):4021-4032.
APA Cheng, Dong,&Kou, Kit Ian.(2018).Generalized sampling expansions associated with quaternion Fourier transform.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,41(11),4021-4032.
MLA Cheng, Dong,et al."Generalized sampling expansions associated with quaternion Fourier transform".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 41.11(2018):4021-4032.
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