INTRODUCTION 5 
input function before being applied to the continuous element. The 
output of this element is the useful output of the system. 
The schematic representation of Fig. 1.3 is intended to show only a 
possible sequence of operations, not necessarily the physical elements 
themselves. For instance, this system could represent a pulse-code 
communications system in which the sampling and coding operation 
is symbolized by the switch. The quantizing aspect of the operation is 
ignored here, since it is assumed that the input is quantized infinitely fine. 
Thus, the input amplitude is presumed to be perfect in this representa- 
tion. The data-reconstruction element reconstructs a continuous signal 
from the sequence of samples as well as is practical. Usually, this can be 
relatively crude, and the physical device takes the form of a simple 
clamp or boxcar circuit. The continuous element is the device which is 
being driven by the reconstructed signal, and its output is the useful 
signal. 
The theory which underlies the performance of this system should 
take into account two deteriorating aspects: the quantizing effect and 
the sampling effect. Both of these tend to distort or deteriorate the 
signal in some way. It is much easier to take into account the effect of 
sampling since it will be shown that this can be described by means of 
linear difference equations. On the other hand, the quantizing effect is 
much more difficult to account for, since it is described by nonlinear 
equations. All the theory in subsequent sections will deal with the linear 
problem, on the assumption that the quantization of the variables is 
made fine enough to produce negligible effect. Generally, the theoretical 
objectives which apply to systems of the type shown in Fig. 1.3 are to 
obtain the output sequence or continuous output in terms of the input 
sequence and the system parameters. 
1.4 The Sampled-data Feedback System 
If the system configuration includes elements which feed the output 
variable back to the input and if a sampling operation is included, the 
system is referred to as a sampled-data feedback system. If the objective 
of the system is to control one or more variables in the system so that 
they have a desired functional relationship with the inputs and disturb- 
ances, the qualifying term control is included in the name. 
A simple sampled-data feedback control system is shown in Fig. 1.4. 
In this system the error signal is sampled and is reconstructed before 
being applied to the continuous element. The latter may be the plant 
or process which is being controlled, including amplifiers, instruments, and 
actuators. This error-sampled system can be compensated by the addi- 
tion of networks in the continuous element, just as in the case of ordinary 
