# One-Dimensional Quaternion Fourier Transform with Application to Probability Theory
> Ekasasmita W.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_85156094472
Jurnal / Konferensi: Symmetry
Tahun terbit: 2023
DOI: https://doi.org/10.3390/sym15040815
ISSN: 20738994
Kuartil SJR: Q2
Citations: 15

## Authors
- Ekasasmita W.

## Abstract
The Fourier transform occupies a central place in applied mathematics, statistics, computer sciences, and engineering. In this work, we introduce the one-dimensional quaternion Fourier transform, which is a generalization of the Fourier transform. We derive the conjugate symmetry of the one-dimensional quaternion Fourier transform for a real signal. We also collect other properties, such as the derivative and Parseval’s formula. We finally study the application of this transformation in probability theory.

## Keywords
- Parseval's theorem
- Fourier inversion theorem
- Fourier transform
- Fractional Fourier transform
- Discrete-time Fourier transform
- Short-time Fourier transform
- Quaternion
- Non-uniform discrete Fourier transform
- Fourier transform on finite groups
- Discrete Fourier transform (general)
- Mathematics
- Generalization
- Fourier analysis
- Algebra over a field
- Mathematical analysis
- Pure mathematics
- Geometry

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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