Daniel Potts, Gabriele Steidl, Manfred Tasche
Fast and stable algorithms for discrete spherical fourier transforms
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

65T99 None of the above but in this section

33C45 Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)

Abstract: In this paper, we propose an algorithm for the stable and efficient
computation of Fourier expansions of square integrable functions on the
unit sphere $S\subset \mathbb{R}^3$, as well as for the evaluation
of these Fourier expansion at special knots. The heart of the algorithm
is an efficiant realization of discrete Legendre function transforms
based on a modified and stabilized version of the Driscall Healy
algorithm.
Keywords: sperical Fourier transform, spherical harmonics, fast legendre function transform, fast cosine transform, cascade summation