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A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform

The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertaint...

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Main Authors: Mawardi Bahri, Samsul Ariffin Abdul Karim
Format: Article
Language:English
Published: MDPI AG 2022
Subjects:
QA76.75-76.765 Computer software
TK7885-7895 Computer engineering. Computer hardware
Online Access:https://eprints.ums.edu.my/id/eprint/42373/1/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/42373/
https://doi.org/10.3390/sym14071303
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spelling my.ums.eprints.423732024-12-23T03:20:34Z https://eprints.ums.edu.my/id/eprint/42373/ A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform Mawardi Bahri Samsul Ariffin Abdul Karim QA76.75-76.765 Computer software TK7885-7895 Computer engineering. Computer hardware The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters. MDPI AG 2022 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/42373/1/FULL%20TEXT.pdf Mawardi Bahri and Samsul Ariffin Abdul Karim (2022) A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform. Symmetry, 14. pp. 1-17. https://doi.org/10.3390/sym14071303
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
topic QA76.75-76.765 Computer software
TK7885-7895 Computer engineering. Computer hardware
spellingShingle QA76.75-76.765 Computer software
TK7885-7895 Computer engineering. Computer hardware
Mawardi Bahri
Samsul Ariffin Abdul Karim
A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
description The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters.
format Article
author Mawardi Bahri
Samsul Ariffin Abdul Karim
author_facet Mawardi Bahri
Samsul Ariffin Abdul Karim
author_sort Mawardi Bahri
title A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
title_short A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
title_full A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
title_fullStr A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
title_full_unstemmed A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
title_sort variation on inequality for quaternion fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform
publisher MDPI AG
publishDate 2022
url https://eprints.ums.edu.my/id/eprint/42373/1/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/42373/
https://doi.org/10.3390/sym14071303
_version_ 1819911291298381824
score 13.244413

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