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<p><b>Abstract</b>—We propose an algebraic framework for the design and implementation of a large class of data-sorting procedures, including all index-digit permutations used in FFTs. We discuss both old and new algorithms in terms of this framework. We show that the algebraic formulation of the new algorithms can be easily encoded using a functional programming language, and that the resulting code introduces no inefficiencies. We present performance results for implementations of three new algorithms for mixed-radix digit-reversal on a Cray C-90 and on a Sun Sparc 5.</p>
Tensor sum, induced permutation, index-digit permutation, mixed-radix digit-reversal.

J. Seguel, J. Feo and D. Bollman, "A Framework for the Design and Implementation of FFT Permutation Algorithms," in IEEE Transactions on Parallel & Distributed Systems, vol. 11, no. , pp. 625-635, 2000.
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