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Convolution theorems associated with quaternion linear canonical transform and applications
Xiaoxiao Hu; Dong Cheng; Kit Ian Kou
2022-08
Source Publicationhttps://www.sciencedirect.com/science/article/abs/pii/S0165168422002821
ISSN0165-1684
Abstract

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are consistent once in complex or real space. Various types of convolution formulas are discussed. Consequently, the QLCT of the convolution of two quaternionic functions can be implemented by the product of their QLCTs, or the summation of the products of their QLCTs. As applications, correlation operators and theorems of the QLCT are derived. The proposed convolution formulas are used to solve Fredholm integral equations with special kernels. Some systems of second-order partial differential equations, which can be transformed into the second-order quaternion partial differential equations, can be solved by the convolution formulas as well. As a final point, we demonstrate that the convolution theorem facilitates the design of multiplicative filters.

KeywordQuaternion Linear Canonical Transform Convolution Theorem Fredholm Integral Equation Quaternion Partial Differential Equations Multiplication Filters
DOI10.1016/j.sigpro.2022.108743
URLView the original
Indexed BySCIE
Language英語English
PublisherSignal Processing
Fulltext Access
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Cited Times [WOS]:0   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorKit Ian Kou
Recommended Citation
GB/T 7714
Xiaoxiao Hu,Dong Cheng,Kit Ian Kou. Convolution theorems associated with quaternion linear canonical transform and applications[J]. https://www.sciencedirect.com/science/article/abs/pii/S0165168422002821,2022.
APA Xiaoxiao Hu,Dong Cheng,&Kit Ian Kou.(2022).Convolution theorems associated with quaternion linear canonical transform and applications.https://www.sciencedirect.com/science/article/abs/pii/S0165168422002821.
MLA Xiaoxiao Hu,et al."Convolution theorems associated with quaternion linear canonical transform and applications".https://www.sciencedirect.com/science/article/abs/pii/S0165168422002821 (2022).
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