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

Didar Urynbassarova and Aajaz A. Teali
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Didar Urynbassarova: National Engineering Academy of the Republic of Kazakhstan, Almaty 050000, Kazakhstan
Aajaz A. Teali: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, India

Mathematics, 2023, vol. 11, issue 9, 1-24

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.

Keywords: quaternion algebra; quaternion Fourier transform; quaternion offset linear canonical transform; convolution; uncertainty principle; swept-frequency filters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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