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A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

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  • Mawardi Bahri
  • Ryuichi Ashino

Abstract

We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

Suggested Citation

  • Mawardi Bahri & Ryuichi Ashino, 2016. "A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:5874930
    DOI: 10.1155/2016/5874930
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    References listed on IDEAS

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    1. Kit Ian Kou & Jian-Yu Ou & Joao Morais, 2013. "On Uncertainty Principle for Quaternionic Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Kit Ian Kou & Jian-Yu Ou & Joao Morais, 2013. "On Uncertainty Principle for Quaternionic Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, April.
    3. Mawardi Bahri & Ryuichi Ashino & Rémi Vaillancourt, 2013. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. 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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    Cited by:

    1. Mawardi Bahri & Muh. Saleh Arif Fatimah, 2017. "Relation between Quaternion Fourier Transform and Quaternion Wigner‐Ville Distribution Associated with Linear Canonical Transform," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
    2. Mawardi Bahri & Ryuichi Ashino, 2019. "A Convolution Theorem Related to Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    3. Mawardi Bahri & Resnawati & Selvy Musdalifah, 2018. "A Version of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2018(1).

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