We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain we derive the convolution theorem associated with the QLCT and obtain a few consequences.
"A Convolution Theorem Related to Quaternion Linear Canonical Transform." Abstr. Appl. Anal. 2019 1 - 9, 2019. https://doi.org/10.1155/2019/3749387