DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

You can consider the entire stopband
of an ideal sinc filter to contain
an infinity of nulls. Mathematically,
the sinc function represents the limit
of Lagrange interpolation as the
order of the polynomial approaches
infinity. See Appendix A of Smith’s
Digital Audio Resampling Home Page,
cited in the margin of page 177.
The 720p60 and 1080i30 standards
have an identical sampling
rate (74.25 MHz). In the logic
design of this example, there is
a single clock domain.
behavior of signals, which are constrained to lie within
a limited range of values forever (say the abstract range
0 to 1 in video, or ±0.5 in audio).
• In signal processing, there is always some uncertainty in
the sample values caused by noise accompanying the
signal, quantization noise, and noise due to roundoff
error in the calculations in the digital domain. When
the source data is imperfect, it seems unreasonable to
demand perfection of an interpolation function.
These four issues are addressed in signal processing by
using interpolation functions that are not polynomials
and that do not come from classical mathematics.
Instead, we usually use interpolation functions based
upon the the sinc weighting function that I introduced
on page 148. In signal processing, we usually design
interpolators that do not “interpolate” the original
sample values.
The ideal sinc weighting function has no distinct nulls in
its frequency spectrum. When sinc is truncated and
optimized to obtain a physically realizable filter, the
stopband has a finite number of nulls. Unlike
a Lagrange interpolator, these nulls do not have to be
regularly spaced. It is the filter designer’s ability to
choose the frequencies for the zeros that allows him or
her to tailor the filter’s response.
Polyphase interpolators
Some video signal processing applications require
upsampling at simple ratios. For example, conversion
from 1280 SAL to 1920 SAL in an HDTV format
converter requires 2:3 upsampling. An output sample is
computed at one of three phases: either at the site of
an input sample, or 1 ⁄3 or 2 ⁄3 of the way between input
samples. The upsampler can be implemented as an FIR
filter with just three sets of coefficients; the coefficients
can be accessed from a lookup table addressed by �.
Many interpolators involve ratios more complex than
the 2:3 ratio of this example. For example, in conversion
from 4f SC NTSC to Rec. 601 (4:2:2), 910 input
samples must be converted to 858 results. This involves
CHAPTER 17 RESAMPLING, INTERPOLATION, AND DECIMATION 181