DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

My explanation describes the
original sampling of an analog
signal waveform. If you are more
comfortable remaining in the
digital domain, consider the
problem of shrinking a row of
image samples by a factor of n
(say, n = 16) to accomplish image
resizing. You need to compute
one output sample for each set of
n input samples. This is the resampling
problem in the digital
domain. Its constraints are very
similar to the constraints of original
sampling of an analog signal.
Filtering and sampling 16
This chapter explains how a one-dimensional signal is
filtered and sampled prior to A-to-D conversion, and
how it is reconstructed following D-to-A conversion. In
the following chapter, Resampling, interpolation, and
decimation, on page 171, I extend these concepts to
conversions within the digital domain. In Image digitization
and reconstruction, on page 187, I extend these
concepts to the two dimensions of an image.
When a one-dimensional signal (such as an audio
signal) is digitized, each sample must encapsulate, in
a single value, what might have begun as a complex
waveform during the sample period. When a
two-dimensional image is sampled, each sample encapsulates
what might have begun as a potentially complex
distribution of power over a small region of the image
plane. In each case, a potentially vast amount of information
must be reduced to a single number.
Prior to sampling, detail within the sample interval
must be discarded. The reduction of information prior
to sampling is prefiltering. The challenge of sampling is
to discard this information while avoiding the loss of
information at scales larger than the sample pitch, all
the time avoiding the introduction of artifacts. Sampling
theory elaborates the conditions under which a signal
can be sampled and accurately reconstructed, subject
only to inevitable loss of detail that could not, in any
event, be represented by a given number of samples in
the digital domain.
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