FFTs for the 2-sphere-improvements and variations

Earlier work by Driscoll and Healy [18] has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this article 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 O(N log(2) N) operations where N is the number of sample points. We also address implementation considerations and give heuristics tor allowing reliable and computationally efficient floating point experiments from our implementation in C on DEC, HP SGI mid Linux Pentium platforms. These results indicate that variations of the algorithm are both reliable and efficient for a large range of useful problem sizes. Performance appears to be architecture-dependent. The article concludes with a brief discussion of a few potential applications.