[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


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 

| From:     Jeroen H. Stessen   | E-mail:  Jeroen.Stessen@xxxxxxxxxxx |
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