[sdiy] jitter analysis

[Magnus Danielson]

From: "Fredrik Carlqvist" <ifrc at iar.se>
Subject: RE: [sdiy] jitter analysis
Date: Fri, 9 Jul 2004 12:18:34 +0200
Message-ID: <200407091018.MAA21549 at pjakkur.iar.se>

> > But another question : are there any dependencies between 
> > the measured standard deviation (SD) of succeeding time 
> > intervals (of each oscillator cycle) and the frequency 
> > of the oscillator ? I.e., low frequency -> high SD, high 
> > frequency -> low SD ? 
>  
> Some of the oscillators show this kind of frequency dependency. I think this
> is because the current in the expco gets very low on low frequencies. The
> noise then gets proportionally larger. Some VCOs don't show this behavior,
> they have the same jitter (measured in SD) on all frequencies. 

Please be advised that standard deviation is an overall measurement, and you
might be interested to investigate other measures, such as power spectrum etc.
Also, due to the non-white noise content in the phase deviation of any
oscillator, for low-frequency modulation you might require to use stronger
statistical tools than standard deviation, such as Allen Deviation, modified
Allen Deviation and Time Deviation (a time-variant of modified Allen
Deviation). The use of RMS measurement on Time Interval Error is also of
interest.

> > And, yet another question : if 44.100 Hz are much too low 
> > to measure this jitter : why can this jitter be audible 
> > (and responsible for "warmer" sounds perhaps) on CD, with 
> > this sampling rate ? Or do you think, it _IS_ not audible 
> > on CD, but only when you hear the synth beeing played life?
> 
> Well, this is what I am trying to find out. My hypothesis is that the sound
> gets fuller with jitter.

Actually, the jitter frequency has probably alot to do with it. Our sensitivity
to jitter have been examined and above 600 Hz it is a rather simple slope
around 1 ns and below where as the tolerance curve drastically rises below
600 Hz due to masking effects. However, it still remains to be validated that
this is indeed what is happening, it's still just a theory (which I have
advocated for).

> I think that physical instruments produce both jitter and phase distortion.
> Think of the violin, the tone is produced by friction between the bow and the
> string. It just cannot have zero SD. And physical sounds are what the ear is
> designed for.

Phase distortion? Jitter is (roughly) another name for phase deviation.
In some cases jitter is the high frequency part and wander is the low frequency
part of the phase deviation a signal has.

> When sampling a tone, the jitter comes along too, but not perfectly. It is
> not possible to measure the jitter with any precision after sampling it at
> 44100Hz. Also, I think most of the psychological effects of the jitter are
> lost when sampling. It is often easy to here the difference between a cello
> played live and one recorded on a CD.

There are many, many more reasons to that then sampling. The chello fills the
room acoustically in a different way then any of the speakers I've seen. This
really colours the sound differently and your recollection of the sound changes
thanks to simple facts like that. In order to compare it you must compare the
chello as played through the same mike and listening in the analog feed and
then through the A/D and D/A conversions and then with *really* good A/Ds and
D/As. Only then can one compare the two situations and make judgements on the
sampling influence. Oh, you better not move the mike either... or the chello.
The way the mike picks up the chello is also important, since that is a
significantly larger influence. To put it simply, it's a bitch to compare,
since already linear properties can change so much.

Cheers,
Magnus