224 SAMPLED-DATA CONTROL SYSTEMS 
with circles and applies to inputs which occur at 7/3, T + (T/3), 
2T + (T/3), . .. and consists of the values g(27/3), g[T + (2T/8)], 
g[2T + (2T/3)], .... Finally, the third sequence, which is marked 
with squares, weights inputs applied at 27/3, T + (27/3), 2T + (27/3), 
.... The sequence of weights for this portion of the input is g(7'/3), 
g(T + (T/38)], g[2T + (T/3)], . ... This peculiarity, a sort of segrega- 
tion of input samples according to their location within a sampling period, 
is a direct consequence of the multirate system with more frequent input 
samples than output samples. In any other case all the inputs are 
treated alike and the simpler methods of earlier chapters apply. 
r(t) 
+ C;(E) 
neat: Ones 
(a) 

Fia. 9.4. Steps in the development of an equivalent circuit to Fig. 9.2 for n = 3 show- 
ing switch decomposition. 
An analysis of the system illustrated by Fig. 9.2 and Fig. 9.3 can be 
obtained by separating the input into three—or n—paths, where all 
samples on a given path will be weighted alike. The separate results are 
added together at the end to give the total output. For example, again 
considering Fig. 9.3, the first sequence of samples, 7(0), r(7), . . - , 1s 
simply obtained by a switch operating at the basic rate of T sec/sample. 
This sequence is weighted by g(0), g(7’), g(2T), . . . and consequently 
may be applied directly to the system G and added in to the output as 
shown in Fig. 9.4a. The summing point has been left to permit inclusion 
of the effects of the other sequences. The second sequence is r(7’/3), 
r[T + (T/3)], r[2T + (7/3)], . . . and is obtained by a sampling switch 
