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Journal of Applied Mathematics
Volume 2014, Article ID 139471, 13 pages
Research Article

On Two-Dimensional Quaternion Wigner-Ville Distribution

Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia

Received 4 August 2013; Revised 24 December 2013; Accepted 24 December 2013; Published 22 January 2014

Academic Editor: Sabri Arik

Copyright © 2014 Mawardi Bahri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.