[sdiy] Moog wander

[Magnus Danielson]

From: René Schmitz <uzs159 at uni-bonn.de>
Subject: Re: [sdiy] Moog wander
Date: Tue, 18 Apr 2006 22:39:13 +0200
Message-ID: <44454E71.3040704 at uni-bonn.de>

Hi again René,

> > When reading up on the jitter tolerances correlated with professional audio (revised
> > recommendations in AES-3id I beleive, and the articles leading up to that) shows that
> > for certain frequencies, jitter well below 1 us may be audioble, just by considering the
> > amplitude of sidebands etc. Most interesting reading and quite seriously done. Not the
> > normal sales-gibberish at least.
> 
> I know how a even a jitter of a lot less than 1us on the *clocks* would 
> lead to artefacts in a digital audio system, because it essentially 
> reduces the resolution of the ADCs and DACs, but isn't the situation 
> here a little different?

Yes and no. For the sigma-delta ADCs and DACs we actually uses, the issue is much more
complex than the simplification that I am about to present, but even under this
simplification (a pure direct & linear DAC or ADC) the effect is present. When you have
a tone being played through a direct & linear 24-bit DAC (oversimplification, we don't
have those lying around usually) a phase-modulation of the sample-rate clock will cause
side-bands of the "perfect tone" (or any other material for that matter). As you get
sufficiently away from the tone itself, the masking effect of the ear will not kill the
side-band off and for that reason (assuming good noise conditions in general) it can be
found that jitter levels of about 1 ns could be audible.

The work was done by the late Julian Dunn and can be found in "Jitter: Specification
and assessment in Digital Audio Equipment" http://www.nanophon.com/audio/jitter92.pdf.
Another interesting article is "Towards Common Specifications for Digital Audio Interface
Jitter" http://www.nanophon.com/audio/towards.pdf which was directly input to
AES-2id-1996 (and not AES-3id as I said previously) and is also referred explicitly from
AES-2id-1996. Other interesting material can be found at http://www.nanophon.com/audio/.

Now, rolling the discussion back to our analogue synths (using the reasoning of subclause
3.2 of jitter92.pdf above) we have a sideband amplitude of Rj = 20log(J*2*pi*f) so
insert your jitter amplitude J (in second) and jitter frequency f of choice and see for
yourself. Weither that will bug you or not depends on the amplitude and jitter frequency
naturally. For large J the approximation doesn't really work, since you need to bring up
your friends of the Bessel polynoms. With sufficient of the good old analogue noise I
think the tolerance is quite high anyway.

Anyway, there you have it. Someone has done the theory for us and it has been validated
as such. Exactly where the limit goes in a real life is a totally different matter, but
here is at least some food for thought.

Cheers,
Magnus