Subject: Re: [linux-audio-dev] RFC: API for audio across network - inter-host audio routing
From: Lamar Owen (lamar.owen_AT_wgcr.org)
Date: Fri Jun 14 2002 - 21:46:33 EEST
On Friday 14 June 2002 01:58 pm, Richard C. Burnett wrote:
> > Which is enough to reconstruct the sine wave if the output is through a
> > proper post-DAC filter.
> amplitude modulation from the different sample points. Have you ever
> plotted a sine wave where you you don't pick enough points to show the
> real shape? It's the same principle.
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.
It follows that as the sampled frequency approaches the Nyquist frequency its
rate of amplitude change must be decreased due to that stubborn upper
sideband. You end up with aliasing distortion from the upper sideband that
passes the Nyquist filtering at the A/D, producing aliasing components
reflected down in frequency. And if you can hear 20kHz (I barely can), you
can detect the difference in attack times for sharply attacking instruments,
which translates as noise, given a 44.1ksps rate.
> But the higher your sampling rate, the more you are guaranteed not to miss
> a max point or a min point, because when the signal is in those ranges,
> it's able to grab many points.
That's what the post-filtering is for. The post-filter acts as an electronic
flywheel that fills in the points between samples. The difficulty is
building accurate output filters -- and that also translates to the cost of
the equipment.
> Actually I read equal to in one of my text books, but that is beside the
> point. It means that you can 'detect' frequencies at that frequency, but
> it doesn't mean you can accuratly reproduce them. Even at say 18kHz
> sampling at 40kz you would see essentially a beat frequency (I think that
> is the term) as the sampling point is different in each cycle, and not
> enough to capture the max/min every time.
The flywheel effect of the post-filter eliminates that. What you do hear is
the aliasing distortion from the loss of the upper sideband of the complex
component of the sampled frequency. A change in amplitude of any given
frequency translates to a static 'carrier' at the frequency of interest and
two sidebands containing the change information. This is AM broadcast theory
here. (I am a broadcast engineer by profession).
> I've done the test. I listened to a CD recorded SACD and a standard CD,
> same CD player. The difference was very audible, and a lot of it to me
> was crispness in the upper frequency range.
Loss of the upper sideband, as the frequency-domain signal acquires components
approaching the Nyquist frequency, might possibly explain this.
> My research indicated that
> clock jitter is the number one cause of problems. This is why there are
> $1000 CD players that do sound different, and their specs usually talk
> about the jitter.
I wholeheartedly agree with that. Jitter causes unmusical (additive instead
of multiplicative) frequency transposition, which in turn creates FM
sidebands in the decoded audio, perceived as 'grunge'. Which is why I spec
broadcast-grade CD players here -- the difference is audible. Plus I get
balanced outputs for RF resistance... :-)
-- Lamar Owen WGCR Internet Radio 1 Peter 4:11
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