The quaternion linear canonical transform (QLCT) has been investigated and used for many years by various research communities; it has been shown to be a powerful tool for signal processing. In this paper, a novel canonical convolution operator and a related correlation operator for QLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation and product theorems are studied.

中文翻译：

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一种新的与四元数线性正则变换相关的卷积、相关和乘积定理

四元数线性正则变换 (QLCT) 已被各个研究团体研究和使用多年；它已被证明是一种强大的信号处理工具。在本文中，提出了一种用于 QLCT 的新型规范卷积算子和相关的相关算子。此外，基于所提出的算子，研究了相应的广义卷积、相关和乘积定理。