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The octonion linear canonical transform: Properties and applications

Author

Listed:
  • Jiang, Nan
  • Feng, Qiang
  • Yang, Xi
  • He, Jin-Rong
  • Li, Bing-Zhao

Abstract

The octonion linear canonical transform (OCLCT) is a generalized form of the octonion Fourier transform (OFT), which in recent years has gradually become a new research area at the intersection of mathematics and signal processing. The study of these transforms not only enriches algebraic content but also provides tools for understanding geometric and physical phenomena in higher dimensions. In this work, we study the properties and potential applications of OCLCTs. First, we derive the differential properties and convolution theorem for the left-sided octonion linear canonical transform (LOCLCT). Second, by utilizing the properties and corresponding convolution theorem, we discuss and analyze 3-D linear time-invariant (LTI) systems. Finally, the examples and simulations provided in this study demonstrate the effectiveness of the proposed transform in capturing LOCLCT-frequency components, highlighting its enhanced flexibility and multiscale analysis capabilities.

Suggested Citation

  • Jiang, Nan & Feng, Qiang & Yang, Xi & He, Jin-Rong & Li, Bing-Zhao, 2025. "The octonion linear canonical transform: Properties and applications," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000529
    DOI: 10.1016/j.chaos.2025.116039
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    References listed on IDEAS

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    1. Mawardi Bahri & Ryuichi Ashino, 2019. "Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle," Journal of Mathematics, Hindawi, vol. 2019, pages 1-13, September.
    2. Rongbo Wang & Qiang Feng & Ding-Xuan Zhou, 2024. "Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations," Journal of Mathematics, Hindawi, vol. 2024, pages 1-11, March.
    3. Didar Urynbassarova & Aajaz A. Teali, 2023. "Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    4. Hehe Yang & Qiang Feng & Xiaoxia Wang & Didar Urynbassarova & Aajaz A. Teali, 2024. "Reduced Biquaternion Windowed Linear Canonical Transform: Properties and Applications," Mathematics, MDPI, vol. 12(5), pages 1-21, March.
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