DATA RECONSTRUCTION 31 
recovery of the original signal from a sample pulse sequence. There 
will always be a ripple component, as well as a certain amount of dis- 
tortion. In addition, the types of signal spectra found in practice are 
rarely limited in frequency content, so that the assumption of a finite 
spectrum is not usually met. Under these circumstances, even a cardinal 

Time, sec. 
Fic. 3.3. Impulsive response of cardinal hold filter. 
data hold will not reproduce the original signal perfectly. For these 
reasons, the cardinal data hold is only of academic interest and will not 
be considered further in the study of practical systems. 
3.2 Polynomial Extrapolation Systems 
As mentioned previously, the process of data reconstruction may be 
viewed as one of extrapolating a signal during a sampling interval, based 
on information given only at past sampling instants. The latter restric- 
tion is necessitated because the input data are samples or values at 
sampling instants only and only past data samples may be used, as 
required by considerations of physical realizability. In carrying out the 
extrapolation of the time function into a sampling interval, it is necessary 
to make an a priori assumption of the form of the function itself. For 
instance, if it is assumed that the function is composed of exponentials, 
then it follows that the extrapolation should be in the form of exponentials 
and that the data-hold system must determine the relative magnitudes 
and exponents which must be used in the particular sampling interval 
under consideration. 
A particular form of extrapolation commonly used in feedback control 
systems is the one which assumes that the original function can be 
approximated by a polynomial in time. The decision which must be 
made a priori is the highest order which is required for an adequate 
extrapolation. Having set this order, the data hold must compute the 
best fit to the past data by adjustment of the coefficients of the various 
terms of the polynomial. If the actual function being reconstructed 
