The Engineer's Guide to Standards Conversion - Snell

SECTION 3 - STANDARDS CONVERSION
3.1 Interpolation
Practical standards conversion takes place in three dimensions as shown above.
For clarity, it is proposed here to begin with a single dimensional system in order to
show the principles clearly. Fig 3.1.1 shows that standards conversion requires a
form of sampling rate conversion where the same waveform must be expressed by
samples at different places. One way of converting is to return to the analogue
domain and simply to sample the analogue signal on a new sampling lattice. There
are many reasons for not doing so, particularly that two additional conversion and
filtering processes add unnecessary quality impairment. In fact a return to the
analogue domain is quite unnecessary as digital interpolation can be used.
Interpolation is the process of computing the value of a sample or samples which lie
off the sampling matrix of the source signal. It is not immediately obvious how
interpolation works as the input samples appear to be points with nothing between
them.
Original analogue
waveform
Input
samples
Output
samples
Fig 3.1.1
Sampling rate conversion consists of expressing the original
waveform with samples in different places.
One way of considering interpolation is to treat it as a digital simulation of a
digital to analogue conversion. According to sampling theory, all sampled systems
have finite bandwidth. An individual digital sample value is obtained by sampling
the instantaneous voltage of the original analogue waveform, and because it has
zero duration, it must contain an infinite spectrum. However, such a sample can
never be seen in that form because the spectrum of the impulse is limited to half of
the sampling rate in a reconstruction or anti-image filter. The impulse response of
an ideal filter converts each infinitely short digital sample into a sinx/x pulse whose
central peak width is determined by the response of the reconstruction filter, and
whose amplitude is proportional to the sample value. This implies that, in reality,
one sample value has meaning over a considerable time span, rather than just at the
sample instant.
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