28 SAMPLED-DATA CONTROL SYSTEMS 
The sampling frequencies which must be used are based on an applica- 
tion of the sampling theorem. While, ideally, signals having limited 
spectra may be sampled at a frequency equal to twice the highest fre- 
quency contained in the signal with no loss of information, practical 
systems always employ much higher sampling frequencies. This is 
necessitated because practical signal spectra are not finite and signal 
recovery filters are not perfect. The practical problem is to select 
sampling frequencies which produce acceptable amounts of distortion 
or ripple. 
The Laplace transform of sampled signals F*(s) can be expressed in 
two general forms. One of these forms can generally be reduced to the 
ratio of finite polynomials in e7:. The other form is an infinite series of 
terms in (s + jwo) and cannot be reduced to a closed expression. Both 
forms find application in the study of sampled-data feedback con- 
trol systems. One of the characteristics of the pulse sequences used in 
sampled-data systems is that signal can be recovered by means of a linear 
filter. This contrasts with carrier systems employed in the field of 
servomechanisms, where nonlinear devices must be used to recover the 
signal. Such systems can be treated as sampled-data systems only after 
the detection process. 
