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Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions
Cheng, Dong; Kou, Kit Ian
2017-12
Source PublicationADVANCES IN APPLIED CLIFFORD ALGEBRAS
ISSN0188-7009
Volume27Issue:4Pages:2961-2983
Abstract

The Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem provides a reconstruction formula for the bandlimited signals. In this paper, a novel kind of the WSK sampling theorem is established by using the theory of quaternion reproducing kernel Hilbert spaces. This generalization is employed to obtain the novel sampling formulas for the bandlimited quaternion-valued signals. A special case of our result is to show that the 2D generalized prolate spheroidal wave signals obtained by Slepian can be used to achieve a sampling series of cube-bandlimited signals. The solutions of energy concentration problems in quaternion Fourier transform are also investigated.

KeywordSpectral Theorem Prolate Spheroidal Wave Function Quaternion Reproducing-kernel Hilbert Spaces Quaternion Fourier Transform Whittaker-shannon-kotel'nikov Sampling Formula
DOIhttps://doi.org/10.1007/s00006-017-0815-x
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000414140500004
PublisherSPRINGER BASEL AG
The Source to ArticleWOS
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Citation statistics
Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationDepartment of Mathematics,University of Macau,Macao,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Cheng, Dong,Kou, Kit Ian. Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS,2017,27(4):2961-2983.
APA Cheng, Dong,&Kou, Kit Ian.(2017).Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions.ADVANCES IN APPLIED CLIFFORD ALGEBRAS,27(4),2961-2983.
MLA Cheng, Dong,et al."Novel Sampling Formulas Associated with Quaternionic Prolate Spheroidal Wave functions".ADVANCES IN APPLIED CLIFFORD ALGEBRAS 27.4(2017):2961-2983.
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