[en] The analytical method for studying the electrodynamic properties of the Josephson transitions, irradiated by the pulse series in form of the Dirac δ-function is developed. The actuality of these studies is related to the possibility of creating the digital-analogous transformers and signal synthesizers of the assigned form with fundamental accuracy on the basis of the Josephson effect. The analytical expressions, determining the conditions of the phase capture, the average voltage on the transition and the Shapiro steps boundaries are obtained. The results are presented in the graphical form for the cases of the unipolar and bipolar pumping of the transition. The discussion of the obtained results and their comparison with the earlier known ones are carried out