Document Type

Technical Report

Publication Date

6-21-1996

Technical Report Number

PCS-TR96-292

Abstract

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.

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