[vorbis-dev] Some random thoughts

[Marshall Eubanks]

Hello All;

Segher Boessenkool wrote:
> 
> > Let me first say that efforts such as Ogg shows there is still a lot of
> > good in mankind, this is truly a great effort!
> 
> Agree eith 2nd, disagree with 1st, I'm afraid. Never has been, either.
> 
> > While I haven't been lurking, I've been looking through the archives to
> > see if this stuff has been discussed before, and I have also tried to read
> 
> "delayed lurking"? :-)
> 
> > the docs, but a few files aren't there yet. That's OK.
> >
> > My primary reason for writing, is a really mindblowing lecture I attended
> > a few weeks ago, given by Professor Jaan Pelt of Tartu Observatory in
> > Estonia. Professor Pelt argued "don't sample regularily!" If you sample
> > regularily, you are limited by the Nyquist theorem, but you're not if
> > you don't, so given a finite number of sampling points, you should sample
> 
> My ears are limited by hardware, uh, wetware.
> 
> > here and there instead of regularily. Research has also been done to
> > figure out an optimal sampling strategy. I have very little training in
> > signal processing, but it occured to me that this should have applications
> > in sound compression. He said that the mathematical basis for this has
> > been known for a few decades but that the principles has seen surprisingly
> > little use in astronomy, physics, computer science and so on (himself (and
> > I) being an astronomer). I thought I'd pass on the idea, just in case...
> 
> Taking the same number of samples as in uniform sampling, but instead
> uniformly random sampled, will increase the Nyquist freq. to at most double
> the normal frequency.

This is actually not true & Kjetil is correct - in the limit, as the
number of
data points -> infinity, a truely randomly sampled time series
will not be band-limited (i.e., will have a spectrum extending up to
infinite frequency). Points to note :

1.) Information is conserved, so for a finite number of samples,
the better view of frequencies above the Nyquist frequency is
balanced by a poorer view of those below (compared to the same number
of uniformly sampled data points).

2.) The sampling has to be truely random for this to work perfectly.

3.) (The killer) : This only works if the data are truely SAMPLED
(i.e., if instantaneous estimates are available). This is a 
mathematical abstraction. Real data are based on time averages over some
interval. If data are sampled at some Nyquist rate, good engineering
would dictate that the "samples" are actually averages over 
~ 1 / Nyquist rate (which will minimize the measurement noise). This will
band-limit the spectrum, so that the random sampled spectrum really
has  little or no extra information over the uniformly sampled one.(It
is also common for this averaging to occur both in the analogue
part of the recording equipment, and in the A to D process.)

Frequently in astronomy, observations (of some star's pulsations, say), really
are much shorter in duration (minutes to hours) than the periods between
measurements (days to weeks), so that these idea really are useful there.
I think that their utility in this case would be basically nil.

> 
> > I guess many Vorbis streams have been sampled long before a Vorbis encoder
> > sees them, either being WAV files, or ripping from CDs. In that case, I
> > thought that one might compress by actually using an irregular subset of
> > the samples, and yet be able restore the sound with good quality. Just a
> > thought.
> 
> Problem is, only random sampling will help us, and then we will have to include
> the sample points in our bitstream.
> 
> I will try to find some stuff about this ireegular sampling, 'cause it's a
> need idea, anyway. Do you have any pointers to papers etc.?
> 
> > Finally, has any thought been given to the possibility of getting the W3C
> > to recommend Vorbis like they did with PNG? Well, it doesn't seem to have
> > helped the adoption of PNG a lot, but it's a thought.
> 
> Not Vorbis, but Ogg.
> Sounds great :-) Maybe they even will do it, 'cause ogg is a container format,
> i.e. anything can be inside (like in png).
> 
> > Keep up the great work!
> 
> Ok, ok, I'll send some useful stuff soon. Been a while...
> 
> Dag dag,
> 
> Segher
> 

                                   Regards
                                   Marshall Eubanks

   Multicast Technologies, Inc.
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