# Two-Dimensional Quaternion Fourier Transform Method in Probability Modeling
> Nurwahidah N.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85188909807
Jurnal / Konferensi: Symmetry
Tahun terbit: 2024
DOI: https://doi.org/10.3390/sym16030257
ISSN: 20738994
Kuartil SJR: Q2
Citations: 7

## Authors
- Nurwahidah N.

## Abstract
The Fourier transform plays a crucial role in statistics, applied mathematics, and engineering sciences. In this study, we give a definition of the two-dimensional quaternion Fourier transform, which is an extension of the two-dimensional Fourier transform. We present a new convolution theorem including this transformation. We study the characteristic function in the setting of quaternion algebra and obtain the essential properties. Based on this, we seek the expected value, variance, covariance, and their basic relations to the two-dimensional quaternion Fourier transform. We illustrate the results by giving examples to see how the obtained results differ from the classical case.

## Keywords
- Quaternion
- Fourier inversion theorem
- Fourier transform
- Mathematics
- Convolution (computer science)
- Discrete-time Fourier transform
- Fractional Fourier transform
- Discrete Fourier transform (general)
- Transformation (genetics)
- Extension (predicate logic)
- Fourier transform on finite groups
- Convolution theorem
- Covariance
- Algebra over a field
- Mathematical analysis
- Fourier analysis
- Pure mathematics
- Computer science
- Statistics
- Geometry
- Artificial intelligence
- Chemistry
- Programming language
- Biochemistry
- Gene
- Artificial neural network

---
Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
Saat mengutip, gunakan DOI bila tersedia atau URL kanonis di atas.