SAMPLED-DATA SYSTEMS 113 
reproductions of the first significant spectrum. The periodicity of the 
frequency-response function merely reflects the fact that a sampled-data 
system is limited in its capacity to transmit a useful spectrum by the 
sampling frequency. A typical sequence of spectra is reproduced from 
the literature! for a second-order sampled-data servomechanism in Fig. 
K(w) c(t 

1.0 

> 
Frequency ae (a) Time 
G(w) c(t) 
ee 
| 
Frequency Tr (b) Time 
t} 
Glw) fs 
eee | 
| 

Frequency = (c) Time 
: 
Frequency i (d) Time 
G(w) c(t) 
i | 
Frequency & (e) Time 
Fic. 5.21. Frequency-response functions and related time-domain response to unit 
step function. 
5.21. In Fig. 5.21a there is a pole located very near the unit circle at 
about one-twentieth the sampling frequency. This means that the pole 
is located on the z plane, with polar coordinates at a radius of almost 
unity and an angle of +18°. The time-domain response to a unit step 
input is experimentally obtained and appears adjacent to the correspond- 
