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arXiv · 2410.19001

Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling

Muhammad Adnan Samad·Yuanqing Xia·Saima Siddiqui·Muhammad Younus Bhat
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Abstract

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

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Muhammad Adnan Samad, Yuanqing Xia, Saima Siddiqui, Muhammad Younus Bhat. 2024-10-18. Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling. https://arxiv.org/abs/2410.19001

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