Subject: RE: [linux-audio-dev] RFC: API for audio across network - inter-h ost audio routing
From: STEFFL, ERIK *Internet* (SBCSI) ("STEFFL,)
Date: Sat Jun 15 2002 - 03:31:51 EEST
> -----Original Message-----
> From: Bob Colwell [mailto:bob.colwell_AT_attbi.com]
> Sent: Friday, June 14, 2002 4:39 PM
> To: linux-audio-dev_AT_music.columbia.edu
> Subject: RE: [linux-audio-dev] RFC: API for audio across network -
> inter-host audio routing
>
>
> Nyquist says that if you sample a repeating waveform, ANY repeating
> waveform, at a sampling rate greater than or equal to the highest
not sure what you mean by 'repeating', it does not have to be periodic, it
just has to be continuous.
> frequency partial present in the waveform, you can exactly duplicate
> that waveform. Yes, exactly duplicate the original.
in theory (i.e. not exactly, it says that you can reconstuct a continuous
function)
reality brings two important factors:
1) the sample we have is not of infinite length -> error is introduced
(see http://www.digital-recordings.com/publ/pubneq.html) - nyquist theorem
is for functions (with no beginning and no end).
2) the real signals are not really limited to exactly half of sample
frequency, the higher frequency (above half the sampling frequency) are
'transformed' into lower frequencies - so the frequencies that you would not
hear in original sound would be in hearing range ion reconstructed signal
(aliasing).
(there might be other reasons why exact signal cannot ber reconstructed)
I don't have time to search for it but I recall something about the
'exact' is not exactly what one would expect, something along the lines that
you don't miss any frequency (when you do fourier transform) but that the
signal you can reconstruct doesn't have exactly the same shape or something
like that...
erik
> Lamar's comments are correct, but then, what difference is there
> between amplitude modulation at the sampling frequency and a partial
> at that frequency? Both contain information that cannot be captured
> by the stated sampling frequency. Why would you amplitude modulate
> anything that fast?
>
> -BobC
>
> -----Original Message-----
> From: linux-audio-dev-admin_AT_music.columbia.edu
> [mailto:linux-audio-dev-admin_AT_music.columbia.edu]On Behalf Of STEFFL,
> ERIK *Internet* (SBCSI)
> Sent: Friday, June 14, 2002 12:01 PM
> To: 'linux-audio-dev_AT_music.columbia.edu'
> Subject: RE: [linux-audio-dev] RFC: API for audio across network -
> inter-host audio routing
>
>
> > -----Original Message-----
> > From: Lamar Owen [mailto:lamar.owen_AT_wgcr.org]
> ...
> > The idea is that you get the integrated value of the
> > amplitude of the sine
> > wave, since a sine wave always has the same shape. But the
> > amplitude, at the
> > Nyquist frequency, cannot change. Yes, I really said that.
> > If the amplitude
> > of the sine wave changes, you get an upper sideband above the
> > Nyquist rate
> > that you cannot sample -- of course you also get a lower
> > sideband that you
> > can sample, but then the recovered envelope is distorted.
> > Amplitude changes
> > at the Nyquist frequency violate Nyquist's theorem. Thus
> the Nyquist
> > frequency itself is an asymptote and cannot be accurately
> > reproduced except
> > in the steady state.
>
> nyquist theorem doesn't say that you can get EXACT same
> signal if your
> sampling frequency is twice the highest frequencey of signal. It says
> (roughly) that you wouldn't miss any bumps (of frequency half of your
> sampling frequency), you can't be sure about the shape of those bump
> (amplitude).
>
> which is basically what you say, it's just that there is no
> violation of
> nyquist theorem there...
>
> erik
>
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