DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Taken literally, decimation involves
a ratio of 10:9, not 10:1.
For details of interpolators and
decimators, see Crochiere, Ronald
E., and Lawrence R. Rabiner,
Multirate Digital Signal Processing
(New York: Prentice-Hall, 1983).
aliasing – and upsampling, where lowpass filtering is
necessary to suppress “imaging.” In signal processing,
the term interpolation generally implies upsampling,
that is, resampling to any ratio of unity or greater. (The
term interpolation also describes phase shift without
sample rate change; think of this as the special case of
upsampling with a ratio of 1:1.)
Downsampling with a ratio of 10:9 is analogous to the
policy by which the Roman army dealt with treachery
and mutiny among its soldiers: One in ten of the
offending soldiers was put to death. Their term decimation
has come to describe downsampling in general.
Lowpass filtering in decimation
Earlier in this chapter, I expressed chroma subsampling
as 2:1 decimation. In a decimator, samples are lowpass
filtered to attenuate components at and above half the
new sampling rate; then samples are dropped. Obviously,
samples that are about to be dropped need not
be computed! Ordinarily, the sample-dropping and
filtering are incorporated into the same circuit.
In the example of halfband decimation for chroma
subsampling, I explained the necessity of lowpass
filtering to 0.25 f S. In the 4f SC NTSC to Rec. 601
example that I presented in Polyphase interpolators, on
page 181, the input and output sample rates were so
similar that no special attention needed to be paid to
bandlimiting at the result sample rate. If downsampling
ratio is much greater than unity – say 5:4, or greater –
then the impulse response must incorporate a lowpass
filtering (prefiltering, or antialiasing) function as well as
phase shift. To avoid aliasing, the lowpass corner
frequency must scale with the downsampling ratio. This
may necessitate several sets of filter coefficients having
different corner frequencies.
CHAPTER 17 RESAMPLING, INTERPOLATION, AND DECIMATION 185