DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Second, FIR filters usually have fixed coefficients; in
a polyphase FIR interpolator, the coefficients vary on
a sample-by-sample basis. Third, typical FIR filters are
symmetrical, but polyphase interpolators are not.
Generally speaking, for a small number of phases –
perhaps 8 or fewer – the cost of an interpolator is
dominated by the number of multiplication operations,
which is proportional to the number of taps. Beyond
about 8 taps, the cost of coefficient storage begins to
be significant. The cost of the addressing circuitry
depends only upon the number of phases.
In the 35:33 downsampler example, I discussed
a hardware structure driven by the input sample rate.
Suppose the hardware design requires that the interpolator
be driven by the output clock. For 31 of each 33
output clocks, one input sample is consumed; however,
for 2 clocks, two input samples are consumed. This
places a constraint on memory system design: Either
two paths from memory must be implemented, or the
extra 44 samples per line must be accessed during the
blanking interval, and be stored in a small buffer. It is
easier to drive this interpolator from the input clock.
Consider a 33:35 upsampler, from Rec. 601 to 4f SC
NTSC. If driven from the output side, the interpolator
produces one output sample per clock, and consumes
at most one input sample per clock. (For 2 of the
35 output clocks, no input samples are consumed.) If
driven from the input side, for 2 of the 33 input clocks,
the interpolator must produce two output samples. This
is likely to present problems to the design of the FIR
filter and the output side memory system.
The lesson is this: The structure of a polyphase interpolator
is simplified if it is driven from the high-rate side.
Decimation
In Lagrange interpolation, no account is taken of
whether interpolation computes more or fewer output
samples than input samples. However, in signal
processing, there is a big difference between downsampling
– where lowpass filtering is necessary to prevent
184 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES