In a book written on the basis of a course of lectures given to students of the GUT named after prof. M.A. Bonch-Bruevich, set forth the theoretical foundations of digital signal processing: methods for describing discrete and digital signals and systems in the time, - and frequency domains, including discrete and fast Fourier transforms, as well as systems in state space; basic methods and features of synthesis of digital linear and adaptive filters; concepts of multi-speed DSP systems.