2019•Unpublished venueRequires access

Relationship Among Three Definitions Of Quaternion Fourier Transforms And Inversion Formula

Mawardi Bahri, Ryuichi Ashino

Abstract

Firstly, based on basic properties of the kernel function of the quaternion Fourier transform we derive in detail relationships among three definitions of the quaternion Fourier transforms. Secondly, based on the quaternion Fourier transform of the quaternion Gaussian function we derive an inversion formula to recovering a quaternion function from the quaternion Fourier transform.

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Available abstract

Key concepts: Quaternion, Fourier transform, Fourier inversion theorem, Mathematics, Fourier series, Fractional Fourier transform, Discrete-time Fourier transform, Discrete Fourier transform (general)