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Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform

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  • Mawardi Bahri
  • Muh. Saleh Arif Fatimah

Abstract

The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT.

Suggested Citation

  • 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, Hindawi, vol. 2017, pages 1-10, September.
    • Handle: RePEc:hin:jnljam:3247364
    DOI: 10.1155/2017/3247364
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