The theory of discrete signal processing. (English. Russian original) Zbl 0538.94001

Berman, S. D.; Grushko, I. I.

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.)

Keywords:

finite group; G-spectrum of a discrete signal; spectral processing of discrete signals