Orthogonal Transforms in Bases of Slant Step Functions. I. Constructing Complete Sets of Orthogonal Slant Step Functions

The author introduces a new class of step functions and defines them in terms of the Rademacher functions. Two complete systems of orthogonal slant step functions are constructed and their characteristics are analyzed. The relationship between the basis functions of these systems and the system of the Walsh functions is established and their orthonormality is proved. It is shown that the proposed systems of slant step functions can be efficiently used to code video signal. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 118–132, May–June 2005.