Remarks on Bandwidth and Regularities in Functions on Finite Non-Abelian Groups

Abstract

Sampling theorem states that under certain conditions, a signal can be reconstructed from data on a restricted area of the domain of definition of the signal model. In this context, the sampling theorem can be discussed also in the case of discrete signals to determine the minimum number of function values needed for the exact determination of a discrete function, with some additional information about the function in the spectral domain. It has been recently shown in that in the case of multiple-valued (MV) functions, the notion of bandwidth relates to the concept of essential variables. Sampling conditions convert into requirements for periodicity and regularity in the truth-vectors of multiple-valued functions. In this paper, we extend these considerations by assuming a finite non-Abelian group as the domain for a given function f to be processed.