One-Dimensional Quaternion Fourier Transform with Application to Probability Theory-Reference-Cited by-同舟云学术

One-Dimensional Quaternion Fourier Transform with Application to Probability Theory

Published:2023-03-28 Issue:4 Volume:15 Page:815
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Ekasasmita Wahyuni¹²^ORCID,Bahri Mawardi¹^ORCID,Bachtiar Nasrullah¹,Rahim Amran¹,Nur Muhammad¹^ORCID

Affiliation:

1. Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia

2. Department of Mathematics, Institut Teknologi Bacharuddin Jusuf Habibie, Parepare 91121, Indonesia

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.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/4/815/pdf

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