[opendtv] Re: Math of oversampling - a REALITY CHECK
- From: Jeroen Stessen <jeroen.stessen@xxxxxxxxxxx>
- To: opendtv@xxxxxxxxxxxxx
- Date: Tue, 3 May 2005 09:06:40 +0200
Hi,
I wrote:
>> Read Watkinson: http://www.microsoft.com/whdc/archive/convrg1.mspx
>> It's more than mere wiggling, it actually makes a lot of sense.
Tom Barry:
> I'm very familiar with that link since I've probably posted it at
> least a half dozen times to this list already.
I had the pleasure of hosting John Watkinson, and his associate
Mikael Reichel (who used to subscribe to OpenDTV) in 1999. He's a
colorful guy, who has said many sensible things about video (and
audio, in Wireless World magazine). Unfortunately for us he seems
to be busy now with writing a "definitive book about helicopters".
> But I confess I've never really understood his math of why display
> resolution should likely be greater. It just seems to work out that way.
JW explains it mostly with the spatial filter characteristics of
square pixel apertures. Such filter has a wide transition band,
meaning that the pass band drops off early and you can't really
use the full resolution of the display (or camera). As you approach
the Nyquist limit of the display (i.e. a pixel-on pixel-off pattern)
you'll get too much difference in response as a function of the
phase in which a pattern is sampled. That's a manifestation of
repeat spectra (or "images"), but if you don't fix it with an
(optical !) low-pass "anti-imaging" filter then it will look more
like aliasing. Better then to eliminate the display as a critical
component by giving it a wider bandwidth than necessary, and do
the low-pass filtering elsewhere. This means: oversampling.
It is similar to audio, where the higher-order analog post-filter
has been replaced with a digital filter that can be realised more
exactly and easier, and the D/A runs at least 4 times faster.
Another argument for oversampling, and I don't think that JW has
mentioned it, has to do with gamma correction. The video signal on
the channel is historically gamma corrected, because that gives the
best distribution of the code space between dark and bright tints.
Gamma correction is done twice, at the camera and at the display.
It is a non-linear operation, so it will distort the spectrum.
A sine wave in gamma space gives a better impression (of sharpness)
than a sine wave in linear-light space, so also in that sense you
can say that the channel is used better. But when we convert a
received signal back to linear-light space (inevitably, because
the spatial reconstruction on the front of screen occurs by
combining light-emitting pixels), then the gamma function creates
higher harmonics. These harmonics belong to the sharpness of the
original signal in the gamma domain, filtering them away will
reduce the sharpness, will reduce the quality of the original
signal. The only way of preserving at least some of these harmonics
is by oversampling, or else they will fold back (aliasing !) into
the baseband. So an oversampled display can help to preserve the
sharpness that is in the original signal. However, I need to assume
that the inverse operation has been applied in the camera, that
the channel spectrum is really optimally filled by applying down-
sampling (in gamma space) at the transmitter side. (And this was
also an assumption at the start of this discussion, right ?!)
Let's not forget that an oversampled display is expensive ! If you
give it more pixels than necessary then there will always be forces
who want to use that extra resolution capability for putting more
information on the display. With audio that wouldn't make much
sense, as our hearing has a hard limit at 20 kHz or less. With
video it depends on the viewing distance, there is no hard limit.
Stationary graphics can afford more resolution than moving video,
so it will be hard to justify oversampling only for video...
Note that the CRT has no inherent problem with (horizontal) aliasing
due to gamma correction, because its gamma function operates in the
time-continuous domain, after D/A conversion and reconstruction
filtering. It is naturally oversampled, contrary to matrix displays.
Best regards,
-- Jeroen
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