You're using an outdated browser. Please upgrade to a modern browser for the best experience.
Quaternion Offset Linear Canonical Transform: Convolution, Correlation, UPs
  • View Times: 54
  • |
  • 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.

Full Transcript
Video Production Service