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Abstract: In this paper we survey some recent work directed towards generalizing the fast Fourier transform (FFT). We work primarily from the point of view of group representation theory. In this setting the classical FFT can be viewed as a family of efficient algorithms for computing the Fourier transform of either a function defined on a finite abelian group, or a bandlimited function on a compact abelian group. We discuss generalizations of the FFT to arbitrary finite groups and compact Lie groups.

Note: This will appear as part of the Proceedings for the 1994 Workshop in Groups and Computation, DIMACS Series of the AMS, edited by Larry Finkelstein and William Kantor.

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   David K. Maslen and Daniel N. Rockmore, "Generalized FFTS - A Survey of Some Recent Results." Dartmouth Computer Science Technical Report PCS-TR96-281, April 1996.

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