[sdiy] jitter analysis

[Magnus Danielson]

From: "Czech Martin" <Martin.Czech at Micronas.com>
Subject: RE: [sdiy] jitter analysis
Date: Fri, 9 Jul 2004 13:22:49 +0200
Message-ID: <D9D56E8FA1A73542BE9A5EC7E35D37FFF390E3 at EXCHANGE2.Micronas.com>

> >  It is
> > not possible to measure the jitter with any precision after 
> > sampling it at
> > 44100Hz. 
> 
> why?
> 
> We're after some effect, the measurment data is only helping
> us to understand. But it is not the real target.
> The target is to understand.
> 
> Perhaps I'm completely wrong, but the ear is somehow a bandpass
> system (fromm my hearing experiments 30 -17000 Hz).
> Above or below I can not tell if a full level tone is on or off
> (headphones).
> 
> If you say that the Nyquist lowpass filtering will allready destroy
> the effect, I suspect that it will also not reach the ear-drum
> or cochlea, since this is allready bandpass filtering, not to speak of
> the nervers and brain.
> 
> So , as long as no profound error in my reasoning can be found,
> it is not clear to me why such obvious effects like livelyhood
> of a wave should not appear in the usual 22050 Hz sampling
> bandwidth.

Let's look at what happends when we phase-modulates a sine with another sine.
The carrier-sine will have give the nominal frequency of the resulted signal.
The modulated sine will produce a series of over and undertones being integer
multiples of the modulated sine frequency, and the amplitude of that sine will
determine the depth of modulation and thus the relative strength of the
sideband tones. Now, the relationship between modulationdepth and sidebandtone
strengths is complex, it's the Bessel function in action there, but for small
modulations we can approximate the first sidebands (fc-fm and fc+fm) as being
proportional to the modulation index m divided by the modulation frequency fm.
Now, if you filter this waveform and lower the sidebands, of course you will
change some of its character. You can lower the jitter of a signal by builing a
very narrow bandpass filter, and when you do it in say SAW technology, then it
is feasable, but instead we tend to use PLLs these days, which acts effectively
as a auto-tuning bandpassfilter where the PLLs bandwidth is half of the
bandwidth this bandpassfilter having (due to the single-side nature of loop
bandwidth and the double-side nature of a bandpass filter).

The ear, being a bandpassesque analyserbank, can naturally sniff the sidebands,
but some of it will be masked by normal masking procedure. Analysis done by
among others the late Julian Dunn has provided insight into where a jitter
tolerance curve would be given the knowledge we have about masking effects and
hearing the sidebands. (I am actually missing the paper, so if someone digs it
out, let me know). This tolerance curve goes below the ns level, just to give
you an indication... I don't recall it in detail right now.

But, here we are going to into another physcoacoustical effect and we then need
the ability to characterise things very carefully in order to be able to
produce any reliable knowledge. If the theory holds, then the amount of
phase deviation for different frequency/time is probably also of importance.

The problem is that when you sample something, and want a finegrained frequency
analysis, you need to compensate for drifts etc. This breaks the analysis with
Fourier transforms fairly quickly. Other means to measure it is better equiped
to record it and with much less information poping out, but better adapted to
the task at hand. This is why I have proposed the use of a finegrained counter
with is able to make back-to-back measurements. This allows one to get a
sampled version of the phase modulation signal to then analyse offline.

> Perhaps the figures you get during measurement must be intepreted
> with keeping in mind that it is bandlimited. Of course.
> But the effect must be somewhere in the samples, otherwise
> it is getting esoteric.

It's not THAT esoteric, there is just a number of measurement methologies and
how accurate they get.

> Hah, this is also the argument that I should have used when Magnus
> told me that 44100 Hz sampling will not allow for precise measurement.
> I mean, he was absolutetly correct!

Thanks! ;O)

> But my question was wrong! It was: How to measure the jitter?
> But it should have been: how to measure the jitter which remains
> after bandpass sampling / lowpass sampling?

I think this boils down to what we think we are going to measure. Do we beleive
it is in the highfrequency or lowfrequency part, I think that a number of old
tricks (slight detuning of oscillators, violas whatever) indicate that it is
not short-term jitter (high frequency) but probably more to the long-term
jitter that we need to look. This is an assumption which seems supported by
numerous experiences, so then doing waveform sampling and fourier analysis does
not seem like the most promessing tool, doing time interval measurements and
log them for further analysis seems like a more promessing tool, especially
since this have been the choice for simular measurements since the 60thies in
the metreological world (such as time and frequency transfer).

We could analyse the impact of the bandlimited sampling on the measurement
result, but I think that would be spending too much time on a detail to a
system I beleive is not well suited in the first place. I think the required
analysis calculation would blow up in your face before you get something
usefull. Also, if we are going to make modifications to some gear to see how
it changes character both to our ear and to the measurement (important point!)
then we can see how the changes of either is relevant or not. This also calls
for a tool with a fairly short round-trip in processing.

Cheers,
Magnus