One-Dimensional Quaternion Fourier Transform with Application to Probability Theory
Wahyuni Ekasasmita, Mawardi Bahri, Nasrullah Bachtiar, Amran Rahim, Muh. Nur
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.
Topics & Concepts
Parseval's theoremFourier inversion theoremFourier transformFractional Fourier transformDiscrete-time Fourier transformShort-time Fourier transformQuaternionNon-uniform discrete Fourier transformFourier transform on finite groupsDiscrete Fourier transform (general)MathematicsGeneralizationFourier analysisAlgebra over a fieldMathematical analysisPure mathematicsGeometryAdvanced Mathematical Theories and ApplicationsMathematical Analysis and Transform MethodsAlgebraic and Geometric Analysis