# A New Form of Convolution Theorem for One-Dimensional Quaternion Linear Canonical Transform and Application
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/a-new-form-of-convolution-theorem-for-one-dimensional-quaternion-linear-canonica
Jurnal / Konferensi: Symmetry
Tahun terbit: 2025
DOI: https://doi.org/10.3390/sym17071004
Kuartil SJR: Q2
Citations: 2

## Authors
- Bahri M.

## Abstract
In this research work, we focus on the one-dimensional quaternion linear canonical transform (1-D QLCT). Under certain conditions, we first derive the symmetry property of the 1-D QLCT for real signals. The new form of the convolution theorem related to this transformation is proposed. We develop this convolution definition to derive the correlation theorem for the 1-D QLCT. We then show that the direct connection between the quaternion convolution and quaternion correlation definitions permits us to provide a different way for proving the correlation theorem concerning the 1-D QLCT. Finally, we present a simple application of the convolution theorem to the study of quaternion swept-frequency filter analysis.

## Keywords
- Convolution (computer science)
- Quaternion
- Mathematics
- Convolution theorem
- Pure mathematics
- Mathematical analysis
- Computer science
- Fourier transform
- Geometry
- Fractional Fourier transform
- Artificial intelligence
- Fourier analysis
- Artificial neural network

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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