42 SAMPLED-DATA CONTROL SYSTEMS 
30 per cent is required. When the velocity correction is zero, the 
extrapolator becomes the zero-order hold and the frequency response in 
the passband is monotonic, as seen in Fig. 3.7. 
While frequency-response characteristics of the data-hold systems 
provide only an indirect indication of performance in the time domain, 
it is generally true that a flat frequency 
response in the region containing the 
significant components produces a bet- 
ter reproduction of the signal than 
does a frequency response which is 
either peaked or excessively drooping. 
Time-domain analyses will confirm 
the results indicated by the frequency- 
response characteristics. Full veloc- 
ity correction produces accurate repro- 
duction of signal only when the input 
signal is a constant or a ramp function. 
If the function being reproduced con- 
tains significant higher-order back differences the errors introduced by using 
a first-order data hold can be reduced by partial velocity correction. <A 
suggested value for this partial correction is about 30 to 50 per cent of the 
velocity as measured by the first back difference. 

Frequency, radians per sec. 
Fig. 3.15. Frequency response of par- 
tial-velocity-correction data hold. 
3.6 Higher-order Data Holds 
Higher-order data holds implement more terms of the Gregory-Newton 
extrapolation formula than the first one or two as described in the previ- 
ous sections. Such systems are potentially capable of reproducing 
higher-order polynomials perfectly after a settling time which depends on 
the number of past samples included in the approximation formula. 
Feedback control systems do not generally utilize these higher-order 
systems, mostly because their excessive phase lags introduce difficulties 
in stabilization of the loop. Even with more effective digital controllers 
the requirement that a number of past samples be received before the 
hold system settles affects the settling time of the entire system adversely. 
Another pertinent factor is that of random noise which may be super- 
imposed on the input data samples to the data hold. Practical systems 
are always subject to random noise, whether it be introduced by external 
influences or by quantization effects in the digital data. If the random 
uncertainties in the value of the data samples are linearly independent, 
then the noise at the output of the data extrapolator is increased as a 
larger number of samples are used in the computation of its output. 
For this reason, higher-order data-hold systems have considerably more 
