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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Didar Urynbassarova & Aajaz A. Teali, 2023. "Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2201-:d:1141074
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    Cited by:

    1. Hehe Yang & Qiang Feng & Xiaoxia Wang & Didar Urynbassarova & Aajaz A. Teali, 2024. "Reduced Biquaternion Windowed Linear Canonical Transform: Properties and Applications," Mathematics, MDPI, vol. 12(5), pages 1-21, March.

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