[opendtv] Re: Math of oversampling
- From: "Don Munsil" <don@xxxxxxxxxx>
- To: <opendtv@xxxxxxxxxxxxx>
- Date: Mon, 25 Apr 2005 10:24:39 -0700
From: "Jeroen Stessen" <jeroen.stessen@xxxxxxxxxxx>
> 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.
Yup - my point exactly.
> 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...
Overshoot is unnatural, but if one only uses a single negative lobe (on a
sinc or sinc-like filter) and the over- and preshoot doesn't get too deep it
contributes to the perception of edge sharpness. Certainly a completely
unsharpened image looks soft to most people.
> 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.
Well, I beg to differ on the first point. If you like, you could use a
two-lobe windowed sinc, but for all intents and purposes, Catmull-Rom is
equivalent to two-lobe Lanczos-windowed sinc. The two curves overlay almost
perfectly. Yes, if you use a bicubic for downsampling you are venturing
outside the original interpolation math because Catmull-Rom was not intended
to be a low-pass filter, but it does work fine. I just use it because it's
equivalent in performance to a windowed sinc but is faster to calculate.
Given that the calculation of the filter kernels is a tiny portion of the
whole scaling operation, it's a false economy, but I just don't see any
reason to switch to windowed sinc.
And yes, I agree completely that you need quite a few taps and a polyphase
filter to get acceptable results. The current scaler I'm working on uses as
many taps and phases as are mathematically necessary, as it's not intended
to be real-time.
> 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.
Agreed.
Best regards,
Don
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