Affiliation:
1. National Engineering Academy of the Republic of Kazakhstan, Almaty 050000, Kazakhstan
2. Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, India
Abstract
Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters.
Funder
Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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