UM
Prolate spheroidal wave functions associated with the quaternionic Fourier transform
Zou C.3; Kou K.I.2; Morais J.1
2018-07-30
Source PublicationMathematical Methods in the Applied Sciences
Volume41
Issue11
Pages4003-4020
AbstractOne 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 © 2017 John Wiley & Sons, Ltd.
Keywordbandlimited extrapolation Mathieu functions quaternionic analysis quaternionic Fourier transform quaternionic signal the energy concentration problem
DOI10.1002/mma.4439
URLView the original
Language英語
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeConference paper
CollectionUniversity of Macau
Affiliation1.Instituto Tecnológico Autonómo de México
2.Universidade de Macau
3.Chengdu University
Recommended Citation
GB/T 7714
Zou C.,Kou K.I.,Morais J.. Prolate spheroidal wave functions associated with the quaternionic Fourier transform[C],2018:4003-4020.
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