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

Mawardi Bahri and Muh. Saleh Arif Fatimah

Journal of Applied Mathematics, 2017, vol. 2017, issue 1

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.

Date: 2017
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https://doi.org/10.1155/2017/3247364

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2017:y:2017:i:1:n:3247364

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