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IBM Journal of Research and Development  
Volume 31, Number 2, Page 213 (1987)
Mathematics and Computing
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Fourier transforms that respect crystallographic symmetries

by L. Auslander, M. Shenefelt
In crystallography one has to compute finite Fourier transforms that are often very large and often respect crystallographic symmetries. In this paper we discuss efficient finite Fourier transform algorithms on 5×5×5 points that respect a collection of crystallographic symmetries. Although the size is too small for any practical problems, the methods indicated in this paper can be extended to problems of meaningful size.
Related Subjects: Fourier transforms; Mathematics