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1. One-Dimensional Quaternion Fourier Transform with Application to Probability Theory.

Author

Ekasasmita, Wahyuni, Bahri, Mawardi, Bachtiar, Nasrullah, Rahim, Amran, and Nur, Muhammad

Subjects
*QUATERNIONS, *APPLIED mathematics, *FOURIER transforms, *QUATERNION functions, *SCIENTIFIC computing, *CHARACTERISTIC functions
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. [ABSTRACT FROM AUTHOR]

Published
2023
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