DATA RECONSTRUCTION 35 
refreshed by the next impulse. In view of the assumption that the 
sampling intervals are all equal to 7’, the extrapolated value of the func- 
tion should fall to zero 7 sec after the application of the unit impulse 
in order that the next impulse may restore the data hold to its new value. 
r(t), Tp (E) 

Fia. 3.4. Reconstruction of r(¢) by a zero-order data hold. 
The impulsive response of the zero-order data hold should therefore 
appear as shown in Fig. 3.5. 
To obtain the transfer function of this system, the impulsive response 
&,(t) 
&)(\t) : 
1.0 +1,0 

T Time 
—1.0 
0 T 
Time 
Fic. 3.5. Impulsive response of a zero- Fic. 3.6. Step-function components of im- 
order data hold. pulsive response of zero-order data hold. 
can be decomposed into two unit step functions, as shown in Fig. 3.6. 
The impulsive response is given by 
g(t) = u(t) — u(t — T) (3.13) 
where u(t) is the unit step function. The Laplace transform of g;(é) is 
1 
Geom - — lem (3.14) 
This transfer function is useful in the analysis of systems which include 
