THE SAMPLING PROCESS Pail 
This spectrum is plotted in Fig. 2.9, where the familiar sideband spectra 
in the signal at the output of the modulator are seen. This form of 
modulation is the one found in most carrier-suppressed data systems used 
in feedback control devices. 
The important characteristic to note is that the total spectrum does 
not contain the signal spectrum, so that no linear filter can possibly 
extract the signal by frequency discrimination or rejection. Demodula- 
tion schemes employing nonlinear devices such as the standard phase 
detector are used to translate the modulated signal spectra. The 
spectrum of a carrier-suppressed modulated signal should be contrasted 
to that obtained with pulse or impulse modulation, as illustrated in 
Figs. 2.6 and 2.7, respectively. The distinctive feature here is that these 
spectra contain the signal spectrum as one of their components, and if 
conditions are correct, a linear wave filter can extract the signal with 
little or no distortion. 
The important difference between the modulated functions p(?) in 
pulse and carrier modulation is that the former function is periodic and 
contains among its various Fourier components a zero-frequency, or d-c, 
term, whereas the carrier function does not. In this manner, the pulse- 
modulation system contains a spectral component which is the unshifted 
signal component resulting in the recoverable signal spectrum. Despite 
these differences, carrier-modulated systems using phase detectors can 
be treated as sampled systems from the point at which demodulation 
takes place and beyond. The phase detector operates on the basis that 
once (or twice) each cycle of the carrier a linear detector charges a load 
condenser to a peak voltage proportional to the amplitude of the latest 
carrier cycle. In this manner, a signal datum is produced once (or twice) 
per cycle of carrier and, in effect, a sampling process of the usual form 
results. The sampling frequency can be considered equal to the carrier 
frequency or twice the carrier frequency, depending on whether a half- or 
full-wave detector is used. 
2.6 Summary 
The sampling operation consists of examining a continuous signal at 
intervals equal to a time 7. The resultant information is a sequence of 
pulses or numbers, each of which gives the value of the signal at a par- 
ticular sampling instant. This sampling process can be considered as a 
modulation process in which the switching function p(t) is a sequence 
of very narrow pulses. For mathematical convenience these pulses can 
be approximated by impulses of the same area for the class of problems 
encountered in feedback control. Properly used, this approximation 
results in mathematical simplifications which are extremely useful in the 
analysis and synthesis of sampled-data systems. 
