[vorbis-dev] Some random thoughts

[Segher Boessenkool]

> 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

You mean measuring over an infinite interval or infinite points in a finite
interval? Second case is trivial, and evly sampled does it as well; first
one surprises me. Need to think some more.

> infinite frequency). Points to note :

[snip]

> 3.) (The killer) : This only works if the data are truely SAMPLED
> (i.e., if instantaneous estimates are available). This is a

This is true for uniform sampling as well, although less devastating
(it's not a killer).

> 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

It will give heavy aliasing into the higher frequency regions, so the
high-frequency part is unusable; to get the continuous signal back from
our sampled signal, we will have to do the band-limiting ourselves.

> 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.)

Unavoidable, I'm afraid.

> 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 see your point. Sounds like fun stuff to work with :-)

> I think that their utility in this case would be basically nil.

Agreed. You can't hear the higher sounds, anyway.

Could it be of any use in the future Ogg video codec?

Dagdag,

Segher

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