Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling
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
Cite
@article{arxiv.2410.19001,
title = {Two-Dimensional Quaternion Linear Canonical Transform A Novel Framework for Probability Modeling},
author = {Muhammad Adnan Samad and Yuanqing Xia and Saima Siddiqui and Muhammad Younus Bhat},
journal= {arXiv preprint arXiv:2410.19001},
year = {2024}
}