INTRODUCTION 11 
to improve accuracy. For instance, in a low-pass system, the output 
contains only a few high-frequency terms, so that the use of output 
sampling as shown in Fig. 1.96 results in less error than with the sampler 
at the error line. In this manner, the numerical method is related to the 
physical system more closely, and the theory applicable to sampled-data 
systems can be used directly. 
1.7 Summary 
The theory of sampled-data systems deals with linear systems in 
which the data appear at one or more points as a pulse sequence or a 
sequence of numbers. The analysis of such systems requires a mathe- 
matical description of the sampling process, of the data-reconstruction 
process, and of the relation between input and output variables, using a 
form of transform calculus known as the z transformation. The latter 
is completely analogous to the Laplace transform as applied to continuous 
systems, and the various theorems, rules, and restrictions are very similar. 
An important advantage of the z transform is that its inversion can be 
carried out directly by means of desk calculators. 
An important feature of sampled-data systems is that they can be 
compensated by means of digital controllers which process number 
sequences rather than continuous time functions. It is possible to obtain 
transient performance whose quality cannot be matched by fully con- 
tinuous systems. The subsequent chapters will be devoted to a develop- 
ment of the underlying theory and application to sampled-data systems, 
particularly feedback systems. The synthesis of sampled-data systems 
which fulfill some specified performance will be an important aspect of 
this development. 
