Technical Report Number
Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper we present a reformulation and variation of the original algorithm which results in a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. All require at most 0(N log2 N) operations where N is the number of sample points. We also address implementation considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. These claims are supported by extensive numerical experiments from our implementation in C on DEC and Sun workstations. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes. The paper concludes with a brief discussion of a few potential appications.
Dartmouth Digital Commons Citation
Healy, D M.; Rockmore, D; and Moore, Sean S.B., "FFTs for the 2-Sphere-Improvements and Variations" (1996). Computer Science Technical Report PCS-TR96-292. https://digitalcommons.dartmouth.edu/cs_tr/134