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Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain

Author

Listed:
  • Mohammad Younus Bhat

    (Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India)

  • Aamir H. Dar

    (Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India)

  • Mohra Zayed

    (Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Altaf A. Bhat

    (University of Technology and Applied Sciences, Salalah 324, Oman)

Abstract

In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and square integrable) functions on R . Later on, we show that 1D-QQPFT satisfies all the respective properties such as inversion formula, linearity, Moyal’s formula, convolution theorem, correlation theorem and uncertainty principle. Moreover, we use the proposed transform to obtain an inversion formula for two-dimensional quaternion quadratic-phase Fourier transform. Finally, we highlight our paper with some possible applications.

Suggested Citation

  • Mohammad Younus Bhat & Aamir H. Dar & Mohra Zayed & Altaf A. Bhat, 2023. "Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain," Mathematics, MDPI, vol. 11(13), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3002-:d:1187655
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    References listed on IDEAS

    as
    1. Mawardi Bahri & Ryuichi Ashino & Rémi Vaillancourt, 2013. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
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