[opendtv] Re: Math of oversampling - a simple comparison

I have sent this mail to Craig, Tom and Bob: 
(the files will probably soon appear on www.trbarry.com) 

Hello, 

At Craig's request: 
> If Tom and Jeroen have time to play, I would like to see a down/up 
> sample pass through 1024 x 576P. 

Here are the results: (2 files deleted) 

file <Leno_1080_576_1080p.jpg> was created 1920x1088 -> 1024x576p 
-> 1920x1088. It is still not quite as sharp as we had hoped ! 

Then I have also made file <Leno_1080_720_1080p.jpg> : 
1920x1088 -> 1280x720p -> 1920x1088. Now that is finally almost 
as sharp as the original. It appears that we need 1280x720 pixels, 
that 1024x576 is just too little for this image. 

(But I am watching this on a 20" CRT in 1600x1200 resolution 
from 1 foot distance, so that is not fair even for HDTV !) 

> My educated guess is that it will be nearly impossible to see 
> the difference from the original.

Well, you seem to have guessed wrong, but why ? 

This morning I have analysed my down- and up-sampling filters, 
and I have determined that the cascade of the two filters has a 
-3 dB point at 73% of the Nyquist limit of the down-sampled image. 
So even if you apply this filter at the original resolution, it 
is still a not neglegible low-pass filter. Unfortunately that is 
the price to pay for low-aliasing scaling, I can't do much better. 
Maybe that is why I need a 25% higher sample rate to get the sort 
of sharpness that you educatedly guessed. 

Regards, 
-- Jeroen 

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