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 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 for...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-05, Vol.11 (9), p.2201
Main Authors: Urynbassarova, Didar, Teali, Aajaz
Format: Article
Language:English
Subjects:
Algebra
Convolution
Dimensional analysis
Fourier transforms
Frequency filters
Graphical representations
Integral transforms
Mathematical research
Mathematics
Principles
quaternion algebra
quaternion Fourier transform
quaternion offset linear canonical transform
Quaternions
Signal processing
swept-frequency filters
Transformations (Mathematics)
uncertainty principle
Uncertainty principles
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11092201