One-Dimensional Quaternion Fourier Transform with Application to Probability Theory
Wahyuni EkasasmitaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaMawardi BahriDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaNasrullah BachtiarDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaAmran RahimDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaMuh. NurDepartment of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
2023en
ABI
Аннотация
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.
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