[sdiy] Analysis of frequency variation in analogue synths

[Magnus Danielson]

From: Nicholas Gregorich <nicksdsu at mac.com>
Subject: Re: [sdiy] Analysis of frequency variation in analogue synths
Date: Mon, 30 Apr 2007 21:41:27 -0700
Message-ID: <289673B3-5228-43C8-87DE-F9E355D96635 at mac.com>

> On Apr 30, 2007, at 4:56 PM, Tom Wiltshire wrote:
> 
> > Hello all,
> >
> > I've just spent an interesting but rather confusing evening trying  
> > to analyse the minor variations in frequency that are supposed to  
> > account for the 'analogue character' of VCOs. I'm hoping to design  
> > a digital oscillator for my monosynth project, and had wondered  
> > about trying to include an 'analogue feel' parameter. As a  
> > precursor to this, I thought I'd better find out what 'analogue  
> > feel' really looks like.
> >
> > Given that I haven't got a full suite of fancy equipment at my  
> > disposal, I sampled some tones from my Pro-One and SH101 into the  
> > computer and then looked at the results with software I wrote to  
> > analyse sound files. This has its limitations, chief among which is  
> > the 44.1KHz (or maybe 48KHz) input sampling of the computer's audio  
> > input.
> 
> I've thought about measuring VCO jitter too. Does the jitter of the  
> ADC have to be measured before assumptions about jitter in the VCO  
> signal can me made?

You need to know you baseline noise-level. Measures near that needs to be
compensated.

> Is there an easy way to measure ADC jitter?

If you have a known quiet source, you could either look at zero-transitions
or FFT and measure sum of sideband energy.

> What kind of distortion does ADC jitter cause in measuring a pure  
> sinusoid anyhow? Is it something you  could see measuring a sine at a  
> known frequency and doing an FFT?

Jitter is rapid phase variation. I say rapid since lower rate variations is
usually denoted wander. Jitter and wander has a fluid border, but for
telecommunication purposes this has been traditionally be set to 10 Hz. That
number is mostly to make a practical sepation between different sources of
phase variation. Phase variations can thus be viewed as the carrier signal
phase modulated with some signal. This creates sidebands and this is well
covered in modulation theory. These sidebands will show up in FFT analysis
if you have sufficient of resolution in amplitude and frequency.

FFT is however limited by non-repetitiveness of the sampled signal in form of
allignment to the FFT "window". This cause spreading of the spikes and will
ruin the noisefloor of a measurement. A windowing function will reduce the
bleeding but not remove it.

The benefit of the FFT method is that white noise is suppressed and sideband
carriers will be integrated. A through zero analysis will be slope limited in
suppressing the through-zero transition as modulated by additive noise. The
cure is gain. The TIC (Time Interval Counters) usually used is somewhat
unfit for the task, since they might have the time resolution for each sample
(I have 200 fs singel-shot resolution in my lab), but noise is a real limiter.
The cure is to provide a slew-rate amplifier package and this has been done
with great succsess.

The topic of weither the jitter & wander aspects is part of the "analog" or
"fattness" has been debated here and elsewhere to death before. I still
consider that issue unsettled. There are parties that argue for the case that
it is or it isn't jitter & wander related. Personally I advocate the point that
it *might* be phase modulations or for that matter amlitude modulations (I
wonder if the ear makes the distinction at lower modulations rates). I have
not seen any conclusive evidence that it is or it isn't. This have been beaten
to death here before, I'm just trying to refer to the issues.

There is much more to be said about this, but I gotta run.

Cheers,
Magnus