INTRODUCTION 3 
widths is not justifiable if some of the cascaded components transmit 
restricted bandwidths. If there are practical advantages to be gained 
by transmitting and processing only a sequence of numbers as opposed 
to a continuous variable, then a proper selection of sampling frequency 
and the use of a sampled-data system seems desirable. 
There are situations when the data-gathering devices themselves are 
capable of producing only discrete sets of numbers rather than a con- 
tinuous variable. For instance, a scanning search radar will generate a 
fix on a target only once every scan. In some large-scale radars, this 
might occur only once every 10 or 15 sec. Between. these scans, or 
“‘looks,”’ no information exists as to ‘the variations in target position. 
Another possibility is the use of time-shared data links in which informa- 
tion can be transmitted only once every cycle time. In such situations, a 
system which incorporates one of these devices as an element is, of neces- 
sity, a sampled-data system. On the other hand, it will be shown later 
that there are certain advantages to be gained by deliberately converting 
a continuous feedback control system into a sampled-data system. The 
use of sampled-data controllers results in systems having dynamical 
performance which cannot be matched by the continuous system from 
which they are derived. 
1.2 Data Reconstruction 
It was stated in the previous section that the continuous function 
from which the number sequence is obtained can be reconstructed by 
processes of interpolation or extrapolation. In numerical computation, 
this is done by using many samples obtained before or after the region 
of interest. On the other hand, real-time dynamical systems can use 
only past samples since the future samples are not known. Thus, data 
reconstruction must be a process of extrapolation using only the preced- 
ing set of samples. This process is sketched in Fig. 1.2, where a continu- 
ous function is being extrapolated from the latest sampling instant at nT. 
The extrapolation in real-time systems is carried out for only one sampling 
interval, extending from n7 to (n + 1)T. Since the value of the function 
is known exactly at the next sampling instant (n + 1)7, this most recent 
value can be used as the base for an extrapolation into the next sampling 
interval. Thus, the extrapolation process is reiterated as each new 
sample becomes available. There are a number of techniques and 
extrapolation formulas which can be used to implement this process. 
In all cases, the objective is to reproduce as well as possible a reasonable 
facsimile of the actual time function from which the sample or number 
sequence was derived. 
The reason why data reconstruction is important in the field of dynam- 
