The Markov–Stieltjes transform of measures and discrete time systems

А class of discrete time filters (systems) with frequency characteristics that are functions of Markov–Stieltjes type is considered. The description of these filters in terms of their system functions and impulse responses is announced. In particular, it is noted that this class contains all filters with completely monotonic impulse responses. The properties of stationarity, causality, stability and reversibility of the corresponding systems are described.