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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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1303 |
| _version_ | 1797415469259423744 |
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| author | Mawardi Bahri Samsul Ariffin Abdul Karim |
| author_facet | Mawardi Bahri Samsul Ariffin Abdul Karim |
| author_sort | Mawardi Bahri |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-09T05:48:04Z |
| format | Article |
| id | doaj.art-54e5328fb2f945b9b08e5f0ce32a705c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:48:04Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-54e5328fb2f945b9b08e5f0ce32a705c2023-12-03T12:19:17ZengMDPI AGSymmetry2073-89942022-06-01147130310.3390/sym14071303A Variation on Inequality for Quaternion Fourier Transform, Modified Convolution and Correlation Theorems for General Quaternion Linear Canonical TransformMawardi Bahri0Samsul Ariffin Abdul Karim1Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaSoftware Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, MalaysiaThe 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.https://www.mdpi.com/2073-8994/14/7/1303uncertainty principlegeneral quaternion linear canonical transformconvolutioncorrelationgeneralized swept-frequency filtersFourier transform |
| spellingShingle | 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 Symmetry uncertainty principle general quaternion linear canonical transform convolution correlation generalized swept-frequency filters Fourier transform |
| title | 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_short | 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 |
| topic | uncertainty principle general quaternion linear canonical transform convolution correlation generalized swept-frequency filters Fourier transform |
| url | https://www.mdpi.com/2073-8994/14/7/1303 |
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