Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs
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• Release Date: 2023-06-01
• quaternion algebra
• quaternion Fourier transform
• quaternion offset linear canonical transform
• convolution
• uncertainty principle
• swept-frequency filters
Video Introduction

This video is adapted from 10.3390/math11092201

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

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Urynbassarova, D.; Teali, A.A. Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs. Encyclopedia. Available online: https://encyclopedia.pub/video/video_detail/745 (accessed on 19 April 2024).
Urynbassarova D, Teali AA. Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs. Encyclopedia. Available at: https://encyclopedia.pub/video/video_detail/745. Accessed April 19, 2024.
Urynbassarova, Didar, Aajaz Ahmed Teali. "Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs" Encyclopedia, https://encyclopedia.pub/video/video_detail/745 (accessed April 19, 2024).
Urynbassarova, D., & Teali, A.A. (2023, June 01). Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs. In Encyclopedia. https://encyclopedia.pub/video/video_detail/745
Urynbassarova, Didar and Aajaz Ahmed Teali. "Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs." Encyclopedia. Web. 01 June, 2023.