Tighter uncertainty principles associated with Bendlet and quaternion-Bendlet transforms
This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter...
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| Published in | Journal of inequalities and applications Vol. 2025; no. 1; pp. 30 - 24 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Springer International Publishing
04.03.2025
Springer Nature B.V SpringerOpen |
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| Abstract | This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs. |
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| AbstractList | This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs. Abstract This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion Bendlet transform (CQBT), respectively, by using the coordinate form for both complex and quaternion signals. We mainly focus on the tighter Heisenberg–Weyl UPs in spatial and directional settings for the CBT and CQBT. Remarkably, these new UPs possess more stringent lower bounds by comparing with the classical UPs. |
| ArticleNumber | 30 |
| Author | Li, Cen Zheng, Shenzhou Wang, Xinyu |
| Author_xml | – sequence: 1 givenname: Cen surname: Li fullname: Li, Cen organization: Locomotive & Car Research Institute, China Academy of Railway Sciences Corporation Limited – sequence: 2 givenname: Xinyu surname: Wang fullname: Wang, Xinyu organization: Department of Mathematics, Beijing Jiaotong University – sequence: 3 givenname: Shenzhou surname: Zheng fullname: Zheng, Shenzhou email: shzhzheng@bjtu.edu.cn organization: Department of Mathematics, Beijing Jiaotong University |
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| Keywords | Continuous quaternion Bendlet transform (CQBT) 42B10 Continuous Bendlet transform (CBT) Tighter Heisenberg-Weyl UP 30G35 94A12 Uncertainty principles (UPs) |
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| Snippet | This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous quaternion... Abstract This paper is devoted to the investigation of several tighter uncertainty principles (UPs) for the continuous Bendlet transform (CBT) and continuous... |
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| SubjectTerms | Analysis Applications of Mathematics Continuous Bendlet transform (CBT) Continuous quaternion Bendlet transform (CQBT) Data compression Fourier transforms Lower bounds Mathematics Mathematics and Statistics Principles Quaternions Tighter Heisenberg-Weyl UP Uncertainty principles Uncertainty principles (UPs) Wavelet transforms |
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| Title | Tighter uncertainty principles associated with Bendlet and quaternion-Bendlet transforms |
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