[sdiy] jitter analysis

[Magnus Danielson]

From: "Cornutt, David K" <david.k.cornutt at boeing.com>
Subject: RE: [sdiy] jitter analysis
Date: Fri, 9 Jul 2004 14:48:13 -0500
Message-ID: <F2907359F3D3E246843DDCA7866656532ECBB9 at xch-se-01.se.nos.boeing.com>

Hi David,

> From: Richard Wentk [mailto:richard at skydancer.com]
> > A 
> > pair of ears are capable of localising transients to a higher 
> > resolution 
> > than you'd expect from the standard 20-20k argument. 
> 
> I'm not too sure about this.  A psychology professor
> once challenged me on this very thing, and demonstrated
> it on me and a few other guinea pigs in the class.
> He used a "clicker" (a children's toy that produces
> a very short transient) to make transients that we
> had to locate while blindfolded.  In the accoustically
> deadened classroom, none of us could locate the transients
> worth a darn.  The only time I got one right was when
> he clicked the clicker under a desk.  That one I was
> able to localize because of the reverberation that
> occurred in the space under the desk.  The instructor's
> point was that sound localization in general, and
> transients in particular, depends heavily on reverb.

I would agree that reverb is a big part of it.

Also, I would not rule out that we also use out eyes to help in the basic
information on how the environment would affect the sound, subconsiously.

> I also have trouble accepting that the human ear can
> perceive any kind of event whose duration is in the
> nanosecond range (is that what you really meant to say,
> Magnus?).

No, I never said that. What I did say was that phase modulation down to
nanosecond scale can be audiable. This is not the same as a transient, it is
a constant phase-modulation with a sine, and the amplitude of that is what is
on the nanosecond-scale but the sidebands they result on is for sure in the
audiorange and it is the relative strengths in relation to the distance which
makes it auditorial.

The relative sideband strength in dB is

            J*w
R  = 20 log    i
 j          ----
             4

Where
Rj is the relative strength of the sideband
J is the jitter amplitude (in time)
wi is the jitter frequency (in radians/seconds)

For a tone at 2 kHz with a jitter level of 1 ns for a 1 kHz jitter frequency we
get the relative strength of

              -9              3                 -6
            10   * 2 * pi * 10           pi * 10
R  = 20 log ------------------- = 20 log --------- = -116.08 dB
 j                   4                       2

This means that if you have this 2 kHz tone with it's 1 kHz phase modulation
with the time amplitude of 1 ns then 1 kHz and 3 kHz will contain the sidebands
of this 2 kHz tone. Considering the dynamics of 24 bit system, this is indeed
mentionable levels. From about 800 Hz where masking effectively stops, there is
a -6 dB slope in tolerans for modulation amplitude with rising modulation
frequency, which is equalent to a constant sideband maximum level. Below 800 Hz
in modulation frequency, the tolerance curve for modulation amplitude rises
quickly due to the masking aspects in the ear.

Now, this is not taken out of the blue, but fairly straiht out of the papers
Julian Dunn has written, among those:

Julian Dunn, "Jitter: Specification and Assessment in Digital Audio Equipment"
(of which parts is is included in AES-2id-1996).

Julian Dunn, "TN-23: Jitter Theory", Audio Precision

I recommend you to get those and other papers of Julian Dunn with friends.

>  This is in the UHF range, and the atmospheric
> absorption at that frequency is tremendous -- it's
> unlikely that anything that short ever reaches our ears.
> Here's a philosophical question: mechanical filter
> systems obey Nyquist with respect to transients.
> What property does the human ear possess that can make
> it invulnerable to the Nyquist limitation?

I think this part of the discussion is irrelevant since they build on the
incorrect understanding of what I meant. I think you will agree with me when
you've looked into the papers etc. as I have referenced.

Actually, just to make the point, Julian Dunn even give the tolerance curve go
below 100 ps in amplitude, so there is food for thought.

Cheers,
Magnus