From: znpt01@trc.amoco.com (Norman P. Tracy)
Subject: Re: Jitter Simulation Program
Originator: znpt01@gpss43
Organization: Amoco Production Company, Tulsa Research
Date: Tue, 12 Jan 1993 16:27:41 GMT


> Following is the jitter Simulation Program written in MATLAB. I don't know
> whether it's accurate but the result of jitter is pretty much like wow&flutter
> If this is the case, then why don't someone try to measure wow&flutter at the
> output of a DAC box driven from a transport?

Kong has a good point here based on actual research. Let's try and place it in
context and correlate it with others work.  I like the analogy to wow&flutter
being a turntable tweeker from way back.  But don't ever expect to hear a
transport/dac produce blatantly audible wow&flutter, any change to pitch has
got to be below the audible threshold of even someone with perfect pitch. How-
ever if you've been around and into audio long enough (I'm dating myself here)
you'll recall the great 'audible differences in turntables' debates.  When
really careful testing was preformed on turntables (here I'm thinking of E.M.
Long's reports in Audio magazine) a correlation between 'inaudible' levels
of wow & flutter and sound quality was discovered.  When Long ran FFTs on the
tones used to measure w&f in addition to a simple meter check he found side-
bands about the desired frequency related to the device under test speed 
stability.  All of these were high quality tt's with inaudible w&f yet Long
reported his listening panel's comments on subjective 'cleanness' correlated
with the sidebands level.

Now back to digital land.  In Harley's Stereophile article (ref. 1) figures
4, 5, & 6 show a computer simulation of a spectrogram of a 10kHz tone. Fig. 4
is with zero jitter, noise is better than -115 db down (all plots show a band
width 20-20000Hz).  In fig. 5 2 nS peak to peak of white noise jitter is added
and the whole noise floor from 20-20000Hz comes up to between -105 and -110db.
In fig. 6 again 2 nS of jitter is added but in this case the jitter is 
sinusoidal at a 1kHz rate.  Now the noise floor is back to -115 db down but
two sidebands at 9kHz and 11kHz appear on either side of the 10kHz test signal.
These sidebands are only -85 db down.  In Harris' AES paper (ref. 2) he obtained
the same results with both simulations and measurements of actual adcs. About
a 10 db decrease in s/n ratio with 2 nS white noise jitter and the appearance
of distortion sidebands about the desired signal when the jitter has a discreet
frequency component.

Now I'll try and but it all together into a THEORY about what's going on.  I
contend its likely that real world transports have jitter levels higher than
2 nS and the jitter contains both white noise and sinusoidal components.  Thus
the jitter degrades both the system's s/n ratio and distortion.  Historically,
as in Long's studies cited above, levels of noise and distortion thought to be
inaudible when analyzed via. a simple meter number have been correlated to
audible effects when more powerful tools like the FFT analyzer have been brought
to bear on the questions raised by careful listeners.  All else being equal 
(which of course it rarely if ever is) the lower the noise and fewer the side-
bands of distortion the 'cleaner', 'clearer', and more 'precise' will be the
reported sound.  Like resonances in a speaker box or tone arm the problem is
not heard as a blatant distortion yet when the cause is removed or modified to
change its character the reproduced music is preceived as cleaner or having a
different character.  Think of real music as apposed to single frequency test
tones.  Jitter will add distortion above and below every frequency component
present in the music up and down the entire audible spectrum.

Norman Tracy


> % Matlab Jitter Simulation / Kong Kritayakirana    1/9/93
>  
> fs = 8*44100;                           % Sampling Frequency in Hz
> f  = 15000;                             % Signal Frequency in Hz
> j  = 000;                               % Standard Deviation of Jitter in ps
>  
> n  = 2048;                              % Number of points to plot
>  
> rand('normal');                         % Set Random Generator to normal 
>  
> timestep = 1/fs;                        % Time step for each sample
> freq = 2*pi*f;                          % 2Pi f  constant
>  
> for i = 1:n,
>      r = rand * j * 1e-9;               % Randomize Jitter Value
>      time = i * timestep + r;           %   and add it to the time base
>      sig(i) = sin (freq*time);
> end
>  
> spectrum = abs(fft(sig));               % Do FFT to get Spectrum
> dBspectrum = 20*log10(spectrum)-60;     % Convert to Decibel
>  
> axis([1 2048 -80 0])
> plot(dBspectrum);
> 

references:
#1 The Jitter Game, Robert Harley; Stereophile January 1993
#2 The Effects of Sampling Clock Jitter on Nyquist Sampling ADCs, and on
Oversampling Delta Sigma ADCs, Steven Harris; Journal Audio Engineering Society,
July 1990
-- 

Norman Tracy

znpt01@trc.amoco.com
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