Мақола

Quaternion Fractional Fourier Transform: Bridging Signal Processing and Probability Theory

Muhammad Adnan SamadElectrical Engineering, Electrical Mechanics and Electrical Technologies Department, Fergana Polytechnic Institute, Fergana 150100, UzbekistanYuanqing XiaSchool of Automation, Beijing Institute of Technology, Beijing 100081, ChinaSaima SiddiquiComputer Engineering and Artificial Intelligence Department, Tashkent University of Information Technologies, Fergana 150100, UzbekistanM. Younus BhatDepartment of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, Awantipora 192122, IndiaDidar UrynbassarovaNational Engineering Academy of the Republic of Kazakhstan, Almaty 050010, KazakhstanAltyn UrynbassarovaFaculty of Information Technology, Department of Information Security, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan

Mathematicsjournal2025en

ABI

Аннотация

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. We further explore the 1DQFRFT’s unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields.

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Мавзулар

Mathematical Analysis and Transform Methods Image and Signal Denoising Methods Digital Filter Design and Implementation

Идентификаторлар

DOI: 10.3390/math13020195

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