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<p>In this paper, we present the two-dimensional quaternion linear canonical transform (2D QLCT) as a novel tool for probability modeling, specifically designed to enhance the analysis of multi-dimensional and complex-valued signals. We develop a comprehensive framework that extends classical probability theory by leveraging the properties of 2D QLCT, providing new insights into probability distributions. The key contributions include the introduction of novel mathematical properties, derivation of the characteristic function in the 2D QLCT domain, and the development of covariance structures within this framework. These results not only broaden the theoretical foundations of probability theory but also offer potential applications across fields such as signal processing, engineering, and statistical analysis.</p>

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Two-dimensional quaternion linear canonical transform: a novel framework for probability modeling

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Muhammad Adnan Samad,
  • Yuanqing Xia,
  • Saima Siddiqui,
  • Muhammad Younus Bhat

摘要

In this paper, we present the two-dimensional quaternion linear canonical transform (2D QLCT) as a novel tool for probability modeling, specifically designed to enhance the analysis of multi-dimensional and complex-valued signals. We develop a comprehensive framework that extends classical probability theory by leveraging the properties of 2D QLCT, providing new insights into probability distributions. The key contributions include the introduction of novel mathematical properties, derivation of the characteristic function in the 2D QLCT domain, and the development of covariance structures within this framework. These results not only broaden the theoretical foundations of probability theory but also offer potential applications across fields such as signal processing, engineering, and statistical analysis.