@inproceedings{7946016c412243cabb6ce34754f47b70,
title = "Ambiguity function and Wigner distribution on the sphere",
abstract = "The ambiguity function and the Wigner distribution are fundamental tools in the time-frequency analysis. In this paper, we present an analog of the ambiguity function and the Wigner distribution for signals on the sphere. First, we formulate the ambiguity function for signals on the sphere which represents the signals in joint spatio-spectral domain and derive an inversion operation to obtain the signal from its ambiguity function. Next, we formulate the Wigner distribution for azimuthally symmetric signals on the sphere as a two dimensional spherical harmonics transform of the ambiguity function. We provide the matrix formulation of the Wigner distribution and discuss some of its useful properties. Finally, we illustrate the use of Wigner distribution for spatial and/or spectral localization of a signal in joint spatio-spectral domain. The obtained results provide the first step in designing more sophisticated transforms on the sphere.",
keywords = "Wigner distribution, ambiguity function, spherical harmonics, unit sphere",
author = "Zubair Khalid and Salman Durrani and Parastoo Sadeghi and Kennedy, {Rodney A.}",
year = "2012",
doi = "10.1109/ICASSP.2012.6288647",
language = "English",
isbn = "9781467300469",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
pages = "3405--3408",
booktitle = "2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings",
note = "2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 ; Conference date: 25-03-2012 Through 30-03-2012",
}