MISCELLANEOUS APPLICATIONS OF SAMPLED-DATA THEORY 309 
for impulse-modulated sequences. This expression is 
+0 
+0 
F*(s) =a » F(s + njwo) = Y feete Ges 5) 
n=0 
n=—0 
This equivalence can be useful in the evaluation in closed form of some 
infinite series. For instance, if the series can be closed more readily in 
e,(0) 

Fig. 11.18. (2) Continuous model giving exact input-output relations for circuit. (6) 
Sampled model which replaces continuous model. 
one of the alternate forms of (11.55) than the other, conversion of the 
series into the preferred form by means of (11.55) is useful. 
The steps in adapting the summation rule consist of first setting 7’, the 
sampling interval, equal to unity. Doing so, 
+ 0 
+c 
» f(nyem" = ) F(s + jn2n) (11.56) 
n=0 
n=—2 
where it will be recalled that wo is equal to 27/T. Selecting a particular 
value of s equal to zero, (11.56) becomes 
+a 
+0 
> Fm) = » F(jn2r) (11.57) 
n=0 
nrn=—e 
