Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical (QOLCT), which is the most general form of QFT with additional free parameters. We explore properties 2D QOLCT, including inversion Parseval formulas, besides relationship other transforms. also examine convolution correlation theorems followed by several uncertainty principles. Additionally, we present an illustrative example proposed transform, demonstrating graphical representation a given signal transformed signal. Finally, demonstrate application where it can be utilized generalize treatment swept-frequency filters.