One dimensional quaternion linear canonical transform in probability theory

• Published in: Signal, image and video processing Vol. 18; no. 12; pp. 9419 - 9430
• Main Authors: Siddiqui, Saima, Samad, Muhammad Adnan, Ismoiljonovich, Fayzullayev Djamshid
• Format: Journal Article
• Language: English
• Published: London Springer London 01.12.2024; Springer Nature B.V
• Subjects: Applications of mathematics; Characteristic functions; Computer Imaging; Computer Science; Fourier transforms; Image Processing and Computer Vision; Multimedia Information Systems; Original Paper; Pattern Recognition and Graphics; Probability theory; Quaternions; Signal,Image and Speech Processing; Statistical analysis; Vision; Quaternion characteristic function; Quaternion linear canonical transform; Quaternion probability density function; Quaternion variance
• ISSN: 1863-1703; 1863-1711
• DOI: 10.1007/s11760-024-03556-9

The quaternion linear canonical transform is considered as central piece in different fields like applied mathematics, engineering, computer sciences, and statistics. In this work, we have introduced the one-dimensional quaternion linear canonical transform, which is a generalization of the quaternion Fourier transform. We explore the characteristic function within the framework of quaternion algebra, elucidating its essential properties. Building on this foundation, we derive the expected value and variance, offering deeper insights into the probabilistic structures associated with the quaternions.