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On Two‐Dimensional Quaternion Wigner‐Ville Distribution

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  • Mawardi Bahri

Abstract

We present the two‐dimensional quaternion Wigner‐Ville distribution (QWVD). The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the classical Wigner‐Ville distribution definition. Based on the properties of quaternions and the QFT kernel we obtain three types of the QWVD. We discuss some useful properties of various definitions for the QWVD, which are extensions of the classical Wigner‐Ville distribution properties.

Suggested Citation

  • Mawardi Bahri, 2014. "On Two‐Dimensional Quaternion Wigner‐Ville Distribution," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:139471
    DOI: 10.1155/2014/139471
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    References listed on IDEAS

    as
    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. Rui-Feng Bai & Bing-Zhao Li & Qi-Yuan Cheng, 2012. "Wigner-Ville Distribution Associated with the Linear Canonical Transform," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, July.
    3. 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.
    4. 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).
    5. 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.
    6. Rui-Feng Bai & Bing-Zhao Li & Qi-Yuan Cheng, 2012. "Wigner‐Ville Distribution Associated with the Linear Canonical Transform," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Mawardi Bahri & Ryuichi Ashino, 2019. "A Convolution Theorem Related to Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).

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