# Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85072726619
Jurnal / Konferensi: Journal of Mathematics
Tahun terbit: 2019
DOI: https://doi.org/10.1155/2019/1062979
ISSN: 23144629
Kuartil SJR: Q3
Citations: 23

## Authors
- Bahri M.

## Abstract
A definition of the two-dimensional quaternion linear canonical transform (QLCT) is proposed. The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the definition of the classical linear canonical transform (LCT). Several useful properties of the QLCT are obtained from the properties of the QLCT kernel. Based on the convolutions and correlations of the LCT and QFT, convolution and correlation theorems associated with the QLCT are studied. An uncertainty principle for the QLCT is established. It is shown that the localization of a quaternion-valued function and the localization of the QLCT are inversely proportional and that only modulated and shifted two-dimensional Gaussian functions minimize the uncertainty.

## Keywords
- Mathematics
- Convolution (computer science)
- Quaternion
- Fourier transform
- Kernel (algebra)
- Fractional Fourier transform
- Convolution theorem
- Uncertainty principle
- Mathematical analysis
- Gaussian
- Pure mathematics
- Fourier analysis
- Geometry
- Artificial intelligence
- Computational chemistry
- Quantum mechanics
- Quantum
- Physics
- Artificial neural network
- Computer science
- Chemistry

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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