Properties and applications of octonion fractional Fourier transform for 3-D octonion signals
Yang X. Feng Q. Jiang N. Bhat M.Y. Urynbassarova D.
October 2025Elsevier Inc.
Digital Signal Processing: A Review Journal
2025#165
In the field of signal processing, especially when dealing with complex signals and multidimensional data analysis requirements, traditional transformation methods often struggle to meet practical application needs. Although the Fourier transform and its derivative methods (such as the fractional Fourier transform) play an important role in signal processing, these methods have obvious limitations in handling high-dimensional non-stationary signals, particularly in capturing the intrinsic structure and time-frequency characteristics of multidimensional signals. To address this issue, this paper proposes a new signal processing tool: the octonion fractional Fourier transform (OFRFT). By systematically studying the differential properties of OFRFT and establishing its convolution theorem, the application of this method in multi-dimensional linear time-invariant systems, including series, parallel, and feedback connections, is thoroughly discussed. Simulation experiments based on octonion signals further verify the practical application value of OFRFT in signal processing. The results demonstrate that OFRFT not only provides a novel theoretical tool for analyzing the time-frequency characteristics of complex signals but also shows significant advantages in non-stationary signal processing, laying an important foundation for theoretical research and engineering applications in related fields.
Convolution theorem , Differential properties , Fractional Fourier transform , Multi-dimensional linear time-invariant systems , Octonion
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School of Mathematics and Computer Science, Yanan University, Shanxi, Yanan, 716000, China
Shaanxi Key Laboratory of Intelligent Processing for Big Energy Data, Shanxi, Yanan, 716000, China
Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, 192122, India
National Engineering Academy of the Republic of Kazakhstan, Almaty, 050000, Kazakhstan
School of Mathematics and Computer Science
Shaanxi Key Laboratory of Intelligent Processing for Big Energy Data
Department of Mathematical Sciences
National Engineering Academy of the Republic of Kazakhstan
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