[opendtv] Re: Sampling Frequency of Image Signals
- From: Jeroen Stessen <jeroen.stessen@xxxxxxxxxxx>
- To: opendtv@xxxxxxxxxxxxx
- Date: Mon, 4 Jun 2007 13:52:41 +0200
Hello,
Dan Grimes wrote:
> "It's also possible to use non-linear quantization to advantage."
> This refers to floating point, no? Or are there new forms of
> non-linear quantization being used?
Like I once said to Prin: "at the end of the day any non-linear
transfer function, like a gamma function, is just a quantisation
table". We were talking about Digital Cinema, where they convert
the linear-light signal to the gamma domain with a pure power law
with an exponent of 1/2.6, and then encode to 12-bits (X',Y',Z').
This function makes the quantization steps approximately equally
visible (or rather: invisible). But under which conditions of eye
adaptation ? It also allocates a lot of codes to intensities that
may never occur in the particular scene, or to parts of the image
that the eye can not adapt to (like a dark window in a bright wall).
I think that you would get better results with an adaptive scale
of lower precision, i.e. a compression-type encoding.
Bert Manfredi:
> Jeroen said that with linear coding, our eyes want at least 14 bits of
> resolution. If the bits are weighted differently, we can do fine with 8
> bits.
Actually, my 14-bits example was the linear-light equivalent of a
10-bits gamma-domain signal. In order to get away with only 8-bits
we would need to have a sufficiently high level of analog noise...
It makes no sense to quantize a noisy signal any more accurate than
the level of its noise. As the signals get cleaner, and our eyes
get more chance to adapt temporally and spatially to the scene
(larger viewing angles !), then we will need more bits.
About the original subject, sampling frequency: anti-aliasing is
needed in order to be able to represent a signal at arbitrary
positions (i.e. in any possible phase). That alone already gives
you the infinite variety of positioning of edges. If not, then
you'll see jitter and moving jaggies on (slow) moving edges, and
that is precisely aliasing. I see a lot of that every day !
A decent anti-aliasing filter (or anti-imaging, for that matter)
with a mild roll-off needs some space for its transition band.
Typically this lies between 1/3 and 1/2 of the sample frequency,
therefore the usable bandwidth is only 1/3 and not 1/2. Nyquist
was an optimist. In audio steeper filters can be used, because
we do not perceive ringing at 20 kHz very well and also the energy
that would kick the filters into such ringing is mostly absent.
So for audio it is not too hard to approach 45% of the sample rate
(20 kHz / 44 kHz). Not so in video: any edge will be surrounded by
ringing. And low-ringing filters are necessarily not steep.
I find it ridiculous that some people put on-off-on-off patterns
(i.e. the Nyquist frequency) on test disks, and then other people
expect that this frequency should pass unattenuated through the
entire system. This frequency can be represented only in two
phases (i.e. 0 and 180 degrees), therefore it can not move...
It is much safer to suppress it entirely than to pass it !
Best,
-- Jeroen
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