DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

I write resampling ratios in the
form input samples:output samples.
With my convention, a ratio less
than unity is upsampling.
Upsampling produces more result samples than input
samples. In audio, new samples can be estimated at
a higher rate than the input, for example when digital
audio sampled at 44.1 kHz is converted to the 48 kHz
professional rate used with video. In video, upsampling
is required in the spatial upconversion from 1280×720
HDTV to 1920×1080 HDTV: 1280 samples in each
input line must be converted to 1920 samples in the
output, an upsampling ratio of 2:3.
One way to accomplish upsampling by an integer ratio
of 1: n is to interpose n-1 zero samples between each
pair of input samples. This causes the spectrum of the
original signal to repeat at multiples of the original
sampling rate. The repeated spectra are called “images.”
(This is a historical term stemming from radio; it has
nothing to do with pictures!) These “images” are then
eliminated (or at least attenuated) by an anti-imaging
lowpass filter. In some upsampling structures, such as
the Langrange interpolator that I will describe later in
this chapter, filtering and upsampling are intertwined.
Downsampling produces fewer result samples than
input samples. In audio, new samples can be created at
a lower rate than the input. In video, downsampling is
required when converting 4f SC NTSC digital video to
Rec. 601 (”4:2:2“) digital video: 910 samples in each
input line must be converted to 858 samples in the
output, a downsampling ratio of 35:33; for each 35
input samples, 33 output samples are produced.
In an original sample sequence, signal content from DC
to nearly 0.5 f S can be represented. After downsampling,
though, the new sample rate may be lower than
that required by the signal bandwidth. After downsampling,
meaningful signal content is limited by the
Nyquist criterion at the new sampling rate – for
example, after 4:1 downsampling, signal content is
limited to 1 ⁄ 8 of the original sampling rate. To avoid the
introduction of aliases, lowpass filtering is necessary
prior to, or in conjunction with, downsampling. The
corner frequency depends upon the downsampling
ratio; for example, a 4:1 ratio requires a corner less than
0.125 f S. Downsampling with an integer ratio of n:1
172 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES