TY - JOUR
T1 - The octonion linear canonical transform
T2 - Properties and applications
AU - Jiang, Nan
AU - Feng, Qiang
AU - Yang, Xi
AU - He, Jin Rong
AU - Li, Bing Zhao
N1 - Publisher Copyright:
© 2025 Elsevier Ltd
PY - 2025/3
Y1 - 2025/3
N2 - 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.
AB - 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.
KW - Convolution theorem
KW - Differential property
KW - Multidimensional linear time-invariant systems
KW - Octonion linear canonical transform
UR - http://www.scopus.com/inward/record.url?scp=85216762313&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2025.116039
DO - 10.1016/j.chaos.2025.116039
M3 - Article
AN - SCOPUS:85216762313
SN - 0960-0779
VL - 192
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 116039
ER -