## FFTs for the 2-Sphere - Improvements and Variations (1996)

Venue: | The Journal of Fourier Analysis and Applications |

Citations: | 104 - 2 self |

### BibTeX

@ARTICLE{Healy96fftsfor,

author = {D.M. Healy and Jr. and D. Rockmore and P. J. Kostelec and Sean S. B. Moore},

title = {FFTs for the 2-Sphere - Improvements and Variations},

journal = {The Journal of Fourier Analysis and Applications},

year = {1996},

volume = {9},

pages = {341--385}

}

### Years of Citing Articles

### OpenURL

### Abstract

Earlier work by Driscoll and Healy [16] has produced an e#cient 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 O(N log 2 N ) operations where N is the number of sample points. We also address implementation considerations and give heuristics for allowing reliable and computationally e#cient floating point implementations of slightly modified algorithms. These claims are supported by extensive numerical experiments from our implementation in C on DEC, HP and SGI platforms. These results indicate that variations of the algorithm are both reliable and e#cient for a large range of useful problem sizes. Performance appears to be architecture-dependent. The paper concludes with a brief discussion of a few potential applications. 1...