Generalized sampling expansions associated with quaternion Fourier transform
Cheng D.; Kou K.I.
Source PublicationMathematical Methods in the Applied Sciences
AbstractQuaternion-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 σ-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 σ-bandlimited quaternion-valued signal in quaternion linear canonical transform sense. Examples are given to illustrate our results. Copyright © 2017 John Wiley & Sons, Ltd.
Keywordconvolution theorem generalized sampling expansions generalized translation quaternion Fourier transform quaternion linear canonical transform Quaternion-valued signals
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Cited Times [WOS]:9   [WOS Record]     [Related Records in WOS]
Document TypeConference paper
CollectionUniversity of Macau
AffiliationUniversidade de Macau
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Cheng D.,Kou K.I.. Generalized sampling expansions associated with quaternion Fourier transform[C],2018:4021-4032.
APA Cheng D.,&Kou K.I..(2018).Generalized sampling expansions associated with quaternion Fourier transform.Mathematical Methods in the Applied Sciences,41(11),4021-4032.
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