# A Variation on Inequality for Quaternion Fourier Transform, Modified Convolution and Correlation Theorems for General Quaternion Linear Canonical Transform
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85133008127
Jurnal / Konferensi: Symmetry
Tahun terbit: 2022
DOI: https://doi.org/10.3390/sym14071303
ISSN: 20738994
Kuartil SJR: Q2
Citations: 6

## Authors
- Bahri M.

## Abstract
The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters.

## Keywords
- Quaternion
- Mathematics
- Convolution (computer science)
- Fourier transform
- Fractional Fourier transform
- Convolution theorem
- Discrete Fourier transform (general)
- Fourier inversion theorem
- Pure mathematics
- Mathematical analysis
- Fourier analysis
- Geometry
- Computer science
- Machine learning
- Artificial neural network

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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