Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform

Mawardi Bahri and Samsul Ariffin Abdul Karim ()
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Mawardi Bahri: Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
Samsul Ariffin Abdul Karim: Software Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia

Mathematics, 2023, vol. 11, issue 5, 1-15

Abstract: Motivated by the fact that the quaternion Fourier transform is a powerful tool in quaternion signal analysis, here, we study the quaternion quadratic-phase Fourier transform, which is a generalized version of the quaternion Fourier transform. We first give a definition of the quaternion quadratic-phase Fourier transform. We derive in detail some essential properties related to this generalized transformation. We explore how the quaternion quadratic-phase Fourier transform is related to the quaternion Fourier transform. It is shown that this relation allows us to obtain several versions of uncertainty principles concerning the quaternion quadratic-phase Fourier transform.

Keywords: quaternion Fourier transform; quaternion quadratic-phase Fourier transform; uncertainty principles (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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