Input-output analysis of multirate feedback systems

A general analytical technique described in this paper permits the extension of Z -transform methods to sampled-data systems containing synchronized switches which do not operate with the same sampling rate. Sampling periods of each switch are first expressed in the form T/p₁. . . T/p₍ (where p₁. . . p₍ are integers not equal to zero) and then it is shown that each switch with a period T/p can be replaced by a system of switches and advance and delay elements where each switch operates with a sampling period T. In this way, the original sampled-data system can be represented by an equivalent system containing switches operating with the same sampling rate. The general solution of such equivalent systems is outlined in this paper.