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Prolate spheroidal wave functions associated with the quaternionic Fourier transform
Zou, Cuiming1; Kou, Kit Ian2; Morais, Joao3
2018-07-30
Source PublicationMATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN0170-4214
Volume41Issue:11Pages:4003-4020
Abstract

One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should therefore be of great interest to find the quaternionic signal whose time-frequency energy distribution is most concentrated in a given time-frequency domain. The present paper finds a new kind of quaternionic signals whose energy concentration is maximal in both time and frequency under the quaternionic Fourier transform. The new signals are a generalization of the classical prolate spheroidal wave functions to a quaternionic space, which are called the quaternionic prolate spheroidal wave functions. The purpose of this paper is to present the definition and fundamental properties of the quaternionic prolate spheroidal wave functions and to show that they can reach the extreme case within the energy concentration problem both from the theoretical and experimental description. The superiority of the proposed results can be widely applied to the application of 4D valued problems. In particular, these functions are shown as an effective method for bandlimited quaternionic signals relying on the extrapolation problem. Copyright (c) 2017 John Wiley & Sons, Ltd.

KeywordQuaternionic Analysis Quaternionic Fourier Transform Quaternionic Signal The Energy Concentration Problem Mathieu Functions Bandlimited Extrapolation
DOIhttp://doi.org/10.1002/mma.4439
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000435802000001
PublisherWILEY
The Source to ArticleWOS
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被引频次[WOS]:1   [WOS记录]     [WOS相关记录]
Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Corresponding AuthorKou, Kit Ian
Affiliation1.School of Information Science and Technology, Chengdu University, Chengdu 610106, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macao, China
3.Department of Mathematics, ITAM, Río Hondo #1, Col. Progreso Tizapan, México, DF 01080, Mexico
Corresponding Author AffilicationFaculty of Science and Technology
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Zou, Cuiming,Kou, Kit Ian,Morais, Joao. Prolate spheroidal wave functions associated with the quaternionic Fourier transform[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2018,41(11):4003-4020.
APA Zou, Cuiming,Kou, Kit Ian,&Morais, Joao.(2018).Prolate spheroidal wave functions associated with the quaternionic Fourier transform.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,41(11),4003-4020.
MLA Zou, Cuiming,et al."Prolate spheroidal wave functions associated with the quaternionic Fourier transform".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 41.11(2018):4003-4020.
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