44 SAMPLED-DATA CONTROL SYSTEMS 
partial velocity correction. The integrator implements this part of the 
process, and its output, when added to the held value r;(nT), produces the 
reconstructed function g(t). Itis seen that a control function is necessary 
in the system because as each sampling instant passes, the stored datum 
in the memory r(n7’) must be transferred to the status of a past sample 
r(n — 1)T. In addition, the integrator must be cleared to zero initial 
condition to be capable of generating a new ramp function for the next 
sampling interval. 
Control function 

Fic. 3.16. Open-cycle first-order data-hold system diagram. 
Data extrapolators of higher complexity than first order can be 
devised, based on this open-cycle system, by the addition of more 
integrators and a memory of more capacity to hold the past samples 
required for the computation. An important point to be noted is that 
the output of the extrapolator depends on the stability of the various 
elements. For instance, if there is a drift component in the integrator, 
it will appear directly in the output. Another complication is the rela- 
tive complexity of the control function which must clear integrators 
and transfer data samples from one position to another in order to main- 
tain the correct ‘“‘age”’ for each sample. The use of feedback methods 
reduces the complexity of this function and results in considerable 
economies, especially for higher-order systems. 
Weighting 
unit 
Fic. 3.17. Porter-Stoneman polynomial extrapolator. 
6(t) 
pe Polynomial 
[> | generator 


e*(t) 

Q(t) 


The feedback technique was first studied by Porter and Stoneman* in 
connection with problems of tracking radar targets. The essential 
principle of the feedback data extrapolator is shown in Fig. 3.17. A 
polynomial generator is incorporated in the system, and its output is 
compared at sampling instants to the input. A prediction error sequence 
e*(t) is generated and applied to a weighting unit. The latter generates 
