Abstract
It is known, that the Shuffle/Exchange-Network (S/E) is well suited to perform the parallel Fast Fourier Transform (FFT). In this paper we show, that it is optimal for this purpose in a quite general sense:
We assume, that a parallel FFT consists of a sequence of (parallel) butterfly-operations on and permutations of the given data vector. It is shown, that only the S/E and a slight variation thereof guarantee a maximum of regularity of the data flow. It follows, that the S/E is best suited for a realisation of a parallel FFT by specialized hardware.
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References
J. Cooley, J. Tukey: An algorithm for machine computation of complex Fourier Series. Math. Comput. 19 (1965), p. 297–301.
D. Kleitman, F. T. Leighton, M. Lepley, G. L. Miller: New Layouts for the Shuffle-Exchange Graph. Proceedings of the 13th Annual ACM Symp. on the Theory of Computing (1981), p. 278–292.
H. Nussbaumer: Fast Fourier Transform and Convolution Algorithms. Springer, Berlin (1981).
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© 1986 Springer-Verlag Berlin Heidelberg
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Wagner, F. (1986). Shuffle/exchange is the natural interconnection scheme for the parallel fast fourier transform. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_189
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DOI: https://doi.org/10.1007/3-540-16811-7_189
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