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/p_{1} ... T/p_{n}
(where
p_{1} ... p_{n}
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.