DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 16.3 Point sampling
runs the risk of choosing an
extreme value that is not
representative of the neighborhood
surrounding the
desired sample instant.
Figure 16.4 Boxcar
weighting function has unity
value throughout one sample
interval; elsewhere, its value
is zero.
Figure 16.5 Boxcar filtering
weights the input waveform
with the boxcar weighting
function: Each output sample
is the average across one
sample interval.
0
1
0
0
0
-0.5 0 +0.5
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Nyquist criterion. The condition is usually imposed by
analog filtering, prior to sampling, that removes
frequency components at 0.5f S and higher. A filter
must implement some sort of integration. In the
example of Figure 16.1, no filtering was performed; the
waveform was simply point-sampled. The lack of
filtering admitted aliases. Figure 16.3 represents the
waveform of an actual signal; point sampling at the
indicated instants yields sample values that are not
representative of the local neighborhood at each
sampling instant.
Perhaps the most basic way to filter a waveform is to
average the waveform across each sample period. Many
different integration schemes are possible; these can be
represented as weighting functions plotted as
a function of time. Simple averaging uses the boxcar
weighting function sketched in Figure 16.4; its value is
unity during the sample period and zero outside that
interval. Filtering with this weighting function is called
boxcar filtering, since a sequence of these functions
with different amplitudes resembles the profile of
144 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES
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