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Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform

Author

Listed:
  • 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
    Data Technologies and Applications (DaTA) Research Group, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia)

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.

Suggested Citation

  • Mawardi Bahri & Samsul Ariffin Abdul Karim, 2023. "Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform," Mathematics, MDPI, vol. 11(5), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1235-:d:1086913
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    References listed on IDEAS

    as
    1. Mawardi Bahri & Samsul Ariffin Abdul Karim, 2022. "Novel Uncertainty Principles Concerning Linear Canonical Wavelet Transform," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    2. Fatin Amani Mohd Ali & Samsul Ariffin Abdul Karim & Azizan Saaban & Mohammad Khatim Hasan & Abdul Ghaffar & Kottakkaran Sooppy Nisar & Dumitru Baleanu, 2020. "Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation," Mathematics, MDPI, vol. 8(2), pages 1-46, January.
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    1. Mawardi Bahri & Samsul Ariffin Abdul Karim, 2022. "Novel Uncertainty Principles Concerning Linear Canonical Wavelet Transform," Mathematics, MDPI, vol. 10(19), pages 1-17, September.

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