One dimensional quaternion linear canonical transform in probability theory
The quaternion linear canonical transform is considered as central piece in different fields like applied mathematics, engineering, computer sciences, and statistics. In this work, we have introduced the one-dimensional quaternion linear canonical transform, which is a generalization of the quaterni...
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| Published in | Signal, image and video processing Vol. 18; no. 12; pp. 9419 - 9430 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Springer London
01.12.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1863-1703 1863-1711 |
| DOI | 10.1007/s11760-024-03556-9 |
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| Abstract | The quaternion linear canonical transform is considered as central piece in different fields like applied mathematics, engineering, computer sciences, and statistics. In this work, we have introduced the one-dimensional quaternion linear canonical transform, which is a generalization of the quaternion Fourier transform. We explore the characteristic function within the framework of quaternion algebra, elucidating its essential properties. Building on this foundation, we derive the expected value and variance, offering deeper insights into the probabilistic structures associated with the quaternions. |
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| AbstractList | The quaternion linear canonical transform is considered as central piece in different fields like applied mathematics, engineering, computer sciences, and statistics. In this work, we have introduced the one-dimensional quaternion linear canonical transform, which is a generalization of the quaternion Fourier transform. We explore the characteristic function within the framework of quaternion algebra, elucidating its essential properties. Building on this foundation, we derive the expected value and variance, offering deeper insights into the probabilistic structures associated with the quaternions. |
| Author | Ismoiljonovich, Fayzullayev Djamshid Siddiqui, Saima Samad, Muhammad Adnan |
| Author_xml | – sequence: 1 givenname: Saima surname: Siddiqui fullname: Siddiqui, Saima email: saimasiddiqui07@gmail.com organization: Department of Mathematics, Fergana Polytechnic Institute – sequence: 2 givenname: Muhammad Adnan surname: Samad fullname: Samad, Muhammad Adnan organization: Electrical Engineering, Electrical Mechanics and Electrical Technologies Department, Fergana Polytechnic Institute – sequence: 3 givenname: Fayzullayev Djamshid surname: Ismoiljonovich fullname: Ismoiljonovich, Fayzullayev Djamshid organization: Department of Mathematics, Fergana Polytechnic Institute |
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| Cites_doi | 10.1007/s00006-007-0037-8 10.1007/s41478-023-00585-4 10.1016/j.amc.2015.09.045 10.1063/1.1665805 10.1007/s10851-007-0004-y 10.1080/17476933.2018.1427080 10.1016/j.ijleo.2021.166914 10.1007/s11760-024-03157-6 10.1016/j.ijleo.2016.09.069 10.3390/math10081217 10.1109/TIP.2006.884955 10.3390/electronics11223775 10.1007/s00006-022-01224-0 10.1007/s00006-013-0412-6 10.1007/s11760-020-01728-x 10.1155/2013/162769 10.1016/j.ins.2017.09.057 10.3390/math11092056 10.3390/sym15040815 10.1007/978-1-4939-3028-9 10.3390/sym14071359 10.1016/j.camwa.2008.05.032 10.1016/j.sigpro.2008.04.012 10.1007/s00034-022-02241-x 10.1111/sapm.12211 10.1007/s00006-015-0620-3 10.1364/JOSA.60.001168 10.1007/978-0-85729-760-0 10.3390/sym16030257 10.1142/S0219691322500357 10.1109/ICWAPR.2012.6294808 |
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| Keywords | Quaternion characteristic function Quaternion linear canonical transform Quaternion probability density function Quaternion variance |
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| SubjectTerms | Applications of mathematics Characteristic functions Computer Imaging Computer Science Fourier transforms Image Processing and Computer Vision Multimedia Information Systems Original Paper Pattern Recognition and Graphics Probability theory Quaternions Signal,Image and Speech Processing Statistical analysis Vision |
| Title | One dimensional quaternion linear canonical transform in probability theory |
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