DATA RECONSTRUCTION 43 
noise in their outputs than do the lower-order systems. This effect 
militates against the use of higher-order data-hold systems in situations 
where the magnitude of the random noise is significant. 
The fact that the plant in control systems is usually low-pass in fre- 
quency response makes the use of overly complex data-hold systems 
unnecessary. The inaccuracies in data extrapolation have been referred 
to as ripple whose frequency components are at sampling frequency and 
higher. For instance, in a zero-order data hold, the staircase approxima- 
tion is seen to differ from the actual continuous function from which the 
pulse sequence is derived by an amplitude-modulated periodic ripple 
component whose fundamental frequency is the sampling frequency. 
While the ripple may cause an undesirable amount of shock at the input 
of the plant, it is nevertheless true that if the plant is low-pass in fre- 
quency response, little of this component appears in the output. For 
this reason, the choice of data hold is largely dictated by the form of the 
function which is to be reconstructed and the capability of the plant to 
accept ripple components at the input without adverse effects. Generally 
speaking, the zero-order data hold is found to be adequate for most 
systems found in practice. In feedback instrumentation devices whose 
major purpose is the reproduction of a signal at low power levels, first- 
order data holds with partial or full velocity correction find application. 
For process-control systems, however, the usual form of data hold used is 
of the zero-order variety. 
3.7 Implementation of Polynomial Extrapolators 
The implementation of polynomial extrapolators generally requires 
the use of devices which are capable of integrating in the time domain. 
The simplest form, the zero-order data hold, can consist of a digital 
register with analogue-to-digital and digital-to-analogue circuits included. 
Other forms include the use of diodes included in circuits known as clamp 
circuits. It is only when first- and higher-order data holds are employed 
that integrators are included as recognizable system elements. As will 
be shown later, higher-order data holds are best implemented with feed- 
back configurations, although it is possible to design open-cycle systems 
also. Because of their simplicity, these will be considered first. 
A block diagram which will implement a first-order hold is shown in 
Fig. 3.16. Here the data samples r(n7) are derived from a function r(¢) 
and are applied to a data clamp, which is, in fact, a zero-order data hold. 
In order to generate the second term of the extrapolation as given in 
(3.17), a ramp function whose slope is the difference between the present 
value, r(nT), and the previous value, r(n — 1)7, must be generated. 
‘The constant k is unity for full velocity correction and less than unity for 
