[opendtv] Re: Math of oversampling

Hi, 

Don Munsil wrote: 
> It's not something that's simply quantifiable. A very clean 
> 480p image gathered with an excellent 480p camera or telecine 
> could be every bit as good as a 1080p image scaled to 480p. 

Maybe. You're comparing optical low-pass filtering with 
electronic (digital) low-pass filtering. The former is done 
in the linear-light domain by a gaussian filter, the latter 
is (probably) done in the gamma domain by a sinc-like filter. 
Both have opportunities for making sampling artefacts, so it 
is impossible to tell a priori which would be best. 

> Practically speaking, the 1080p->480p signal will often look 
> better, largely because of preservation of edge sharpness. 

The electronic sinc-like low-pass filter can have a sharper 
transition band than the optical gaussian filter, and this 
implies that it will create ringing. This ringing contributes 
to the sharpness impression, but it is unnatural too... 

> An image from a 1080p camera downconverted to 480p by a
> good-quality algorithm like bicubic 

That is not a good filter for down-sampling ! You would need 
at least a 12-taps polyphase FIR filter for decent performance. 
You could use a transposed polyphase filter with fewer taps 
(between 4 and 8), see our patent US5892695. The bi-cubic is 
not good enough for transposing, unless you apply some further 
tricks. Better to use a polyphase filter with lookup tables. 

> will probably have better inherent edge sharpness than a 
> raw unsharpened feed of a signal from a 480p camera.

Probably, but it is always a trade-off between sharpness and 
(aliasing) artefacts. Sometimes less sharpness gives better 
pictures. I find that one of the potential attractions of 
HDTV: to give a bit more sharpness for a lot less artefacts. 

> On the other hand, judicious application of quality sharpening 
> algorithms to a native 480p image can quite possibly get it to 
> very nearly the 1080p->480p image. It really depends on the 
> cameras, the algorithms, the various formats the picture goes 
> through, etc.

We call that PixelPlus, and every major manufacturer has his 
own version of such algorithms. Sony started it with DRC. 

Greetings, 
-- Jeroen 

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