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The theory of discrete signal processing. (English. Russian original) Zbl 0538.94001
Probl. Inf. Transm. 19, 284-288 (1983); translation from Probl. Peredachi Inf. 19, No. 4, 43-49 (1983).
Summary: Assume that G is a finite group. A general definition of the G-spectrum of a discrete signal, that utilizes irreducible representations of group G, is given. If G is an Abelian group, then the G-spectrum coincides with the familiar definition. The general definition of G-spectrum preserves all the advantages of spectral processing of discrete signals that are inherent in the Abelian case. For lengths that are powers of 2, an infinite sequence $$\{G_ n\}$$ of non-Abelian groups is constructed, for which the $$G_ n$$-spectrum can be calculated 3/4 times more rapidly than the FFT allows in the Abelian case for the same lengths.

##### MSC:
 94A12 Signal theory (characterization, reconstruction, filtering, etc.)