DATA RECONSTRUCTION 51 
As in all extrapolation processes, an a priori assumption is made as to 
the class of function which best fits the input function. For instance, 
one of the most common forms of extrapolation used in sampled-data 
systems is one which assumes that the input function is or can be approxi- 
mated by a polynomial in time. For practical reasons, this polynomial 
contains a finite number of terms whose coefficients are computed within 
the data-hold element. The zero-order data hold uses only the zeroth- 
order term of the polynomial, thereby deriving its name. In practice, 
it is rare to find data holds which implement anything higher than the 
first-order term. Aside from the question of complexity, the reason for 
this is that feedback systems are usually low pass, and their stability is 
adversely affected by the increased phase lags found in the frequency 
response of higher-order data holds. 
The use of a feedback implementation for polynomial data holds has a 
number of advantages, the most important of which is that it does not 
require the storage of data samples in elements such as tapes or drums, 
as would be the case with open-cycle implementations. The feedback 
extrapolator can be implemented using only continuous integrators of 
the electronic or mechanical variety. In the case of the zero-order data 
hold, implementation by simple elements such as diodes and capacitors 
is possible. It is only in higher-order systems that the more complex form 
of implementation must be used. 
Low-pass passive networks can be used as data holds. A simple resist- 
ance-capacitance network is shown to approximate the zero-order data 
hold. Even better approximations can be obtained by the use of more 
passive elements, including inductances as well as resistances and capaci- 
tances. The criteria which govern the degree of complexity which is used 
in feedback control applications are generally the amount of ripple which 
the plant can accept without damage to itself and the amount of jitter 
at ripple frequencies which can be tolerated in the controlled variable. 
It is true, however, that relatively unsophisticated methods of data recon- 
struction are adequate in most practical control-systems applications. 
