CHAPTER 3 
DATA RECONSTRUCTION 
A sampled time function bears little resemblance to the original func- 
tion from which it is derived. While the envelope of the sampled func- 
tion corresponds to the values of the continuous function at sampling 
instants and may appear to be similar on cursory examination, the wide 
divergence between the two functions becomes more evident on the basis 
of frequency spectra. The sampled function contains spurious side 
spectra introduced by the sampling process. A linear low-pass wave 
filter can be used to extract the signal spectrum to a certain degree of 
accuracy. The errors are caused by the overlapping frequency spectra 
and by the nonideal filtering characteristics of practical filter networks, 
which do not completely attenuate the side spectra. 
In this application, a filter which extracts the signal spectrum may be 
thought of as a data-reconstruction device or data extrapolator. In 
effect, the filter does extrapolate a continuous time function into a 
sampling interval based on the weighted average effects of previous 
samples. The deviations of this extrapolated time function from the 
actual function from which the samples were derived is called the “‘ripple”’ 
in the output. From a practical viewpoint, there are good reasons why 

Fig. 3.1. Typical error-sampled feedback control system. 
the ripple must be maintained below a certain level. The plant in a 
system is subjected to command signals which contain ripple components. 
If they are excessive, the plant components are subject to wear, noise, and 
unnecessary wastage of control effort. For this reason, the study of data 
holds used for signal reconstruction must consider this effect as an 
important engineering design factor. 
In typical feedback control systems, the data-reconstruction element is 
generally referred to as the ‘data hold,” “‘desampling filter,” or “data 
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