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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19001 |
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| _version_ | 1866929557927362560 |
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| author | Samad, Muhammad Adnan Xia, Yuanqing Siddiqui, Saima Bhat, Muhammad Younus |
| author_facet | Samad, Muhammad Adnan Xia, Yuanqing Siddiqui, Saima Bhat, Muhammad Younus |
| contents | The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as signal processing, optics, and quantum mechanics. Extending this concept to quaternion algebra, the Quaternion Fourier Transform (QFT) emerged, enriching the analysis of multidimensional and complex-valued signals. The Quaternion Linear Canonical Transform (QLCT), a further generalization, has now positioned itself as a central tool across various disciplines, including applied mathematics, engineering, computer science, and statistics. In this paper, we introduce the Two Dimensional Quaternion Linear Canonical Transform (2DQLCT) as a novel framework for probability modeling. By leveraging the 2DQLCT, we aim to provide a more comprehensive understanding of probability distributions, particularly in the context of multi-dimensional and complex-valued signals. This framework not only broadens the theoretical underpinnings of probability theory but also opens new avenues for researchers |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling Samad, Muhammad Adnan Xia, Yuanqing Siddiqui, Saima Bhat, Muhammad Younus Functional Analysis The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as signal processing, optics, and quantum mechanics. Extending this concept to quaternion algebra, the Quaternion Fourier Transform (QFT) emerged, enriching the analysis of multidimensional and complex-valued signals. The Quaternion Linear Canonical Transform (QLCT), a further generalization, has now positioned itself as a central tool across various disciplines, including applied mathematics, engineering, computer science, and statistics. In this paper, we introduce the Two Dimensional Quaternion Linear Canonical Transform (2DQLCT) as a novel framework for probability modeling. By leveraging the 2DQLCT, we aim to provide a more comprehensive understanding of probability distributions, particularly in the context of multi-dimensional and complex-valued signals. This framework not only broadens the theoretical underpinnings of probability theory but also opens new avenues for researchers |
| title | Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.19001 |