Slant Rademacher functions: properties and application to the problems of digital signal processing

A systems class of discrete functions considered as a generalization of the classical discrete Rademacher system is suggested. Properties of the suggested systems of discrete functions and their application to algorithm synthesis of digital signal processing are considered. The suggested systems of the slant Rademacher functions and their modifications allow to extend the algorithmic possibilities of solving some problems of digital signal processing in the one-dimensional and multi-dimensional statements. The known algorithms oriented to the implementation by means of binary arithmetic are generalized to the case of using r-array arithmetic (r>2).