V.F. Kravchenko, O.V. Kravchenko, V.I. Pustovoit, D.V. Churikov
The review is devoted to 40-year anniversary of the theory of atomic functions (AF) and also to WA-systems of the functions con-structed on their basis with reference to a wide class of problems of digital signal processing, radio physicists, antenna technique, electrodynamics and gyroscope. AF are natural expansion of elementary functions class which became necessary now when have widely started to be applied finite functions. They are expedient for applying in numerical methods there where approximated function possesses probably smoothness and where application of high degree polynomial is complicated because of them non-finiteness. AF can will find wide application in other areas of mathematics. Some applications of the theories of AF, WA-systems of functions and R-functions in modern problems of radio physics and techniques are considered. The attention is concentrated mainly to applications of AF to digital signal and image processing, problems of the antenna analysis and synthesis, probability theory, boundary value problems of mathematical physics.