TY - JOUR
T1 - Probabilistic representation of high-dimensional random signals via octonion linear canonical transform
AU - Jiang, Nan
AU - Feng, Qiang
AU - Yang, Xi
AU - Li, Bing Zhao
AU - Kumar, Manish
N1 - Publisher Copyright:
© 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
PY - 2026/10
Y1 - 2026/10
N2 - The octonion linear canonical transform (OCLCT) extends the traditional linear canonical transform (LCT) to the octonion algebra, enabling effective processing of higher-dimensional signals. Emerging as a cutting-edge tool for high-dimensional signal analysis, OCLCT offers enhanced capabilities for handling high-dimensional non-stationary signals. This paper explores the properties of OCLCT and introduces probability theory in the OCLCT domain. Firstly, the basic properties of OCLCT, such as boundedness, parity, and shift, are presented, and the convolution theorem of OCLCT is also derived. Secondly, we establish the probabilistic framework for OCLCT, defining the mean, characteristic function in the octonion domain. In addition, the probability theory in the three-dimensional OCLCT domain is also discussed. Finally, numerical simulations validate the proposed theory, including characteristic function computation and distribution visualization for octonion-valued densities.
AB - The octonion linear canonical transform (OCLCT) extends the traditional linear canonical transform (LCT) to the octonion algebra, enabling effective processing of higher-dimensional signals. Emerging as a cutting-edge tool for high-dimensional signal analysis, OCLCT offers enhanced capabilities for handling high-dimensional non-stationary signals. This paper explores the properties of OCLCT and introduces probability theory in the OCLCT domain. Firstly, the basic properties of OCLCT, such as boundedness, parity, and shift, are presented, and the convolution theorem of OCLCT is also derived. Secondly, we establish the probabilistic framework for OCLCT, defining the mean, characteristic function in the octonion domain. In addition, the probability theory in the three-dimensional OCLCT domain is also discussed. Finally, numerical simulations validate the proposed theory, including characteristic function computation and distribution visualization for octonion-valued densities.
KW - Characteristic function
KW - Convolution theorem
KW - Octonion distribution function
KW - Octonion linear canonical transform
KW - Probability theory
UR - https://www.scopus.com/pages/publications/105038018622
U2 - 10.1016/j.sigpro.2026.110676
DO - 10.1016/j.sigpro.2026.110676
M3 - Article
AN - SCOPUS:105038018622
SN - 0165-1684
VL - 247
JO - Signal Processing
JF - Signal Processing
M1 - 110676
ER -