An alternative to Slepian functions on the unit sphere - A space-frequency analysis based on localized spherical polynomials
Abstract
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on the one hand, and to the theory of Slepian functions on the 2-sphere on the other. Results from both theories are used to prove localization and approximation properties of the new band-limited yet space-localized basis. Moreover, particular weak limits related to the structure of the spherical harmonics provide information on the proportion of basis functions needed to approximate localized functions. Finally, a scheme for the fast computation of the coefficients in the new localized basis is provided.
Cite
@article{arxiv.1307.3862,
title = {An alternative to Slepian functions on the unit sphere - A space-frequency analysis based on localized spherical polynomials},
author = {Wolfgang Erb and Sonja Mathias},
journal= {arXiv preprint arXiv:1307.3862},
year = {2013}
}
Comments
25 pages, 4 figures