about jitter... (digital does NOT mean perfect)

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ouch, some mails from the list get caught in the spam filter. 
This will be a very late answer... :-(

On Thursday 22 November 2007 20:49, you wrote:

> Just a random thought on jitter - if you like music recorded originally
> before the digital era - don't bother.
>
> I.e. analog tape recorder wow and flutter
[...]
> is much higher than digital jitter.

sorry, though it MAY seem that these are somewhat similar/related 
problems, they are in fact completely different "beasts".

The W&F is due to slight, "random" variations (fluctuations) of the 
tape (or disk) speed during audio recording and/or reproduction that
in turn cause corresponding variations of the general "pitch" of the 
recorded and/or reproduced music.

It's effect is sort of like the same that you would fill due to 
Doppler effect if you and the sound source would be moving back 
and forth with respect to each other.

With bad devices (bad or too cheap tape decks or turntables) it's 
immediately identifiable and rather annoying, but with good enough 
equipment it's so small that it is negligible - if at all audible.

(consider that you'd get similar Doppler effects if you move your 
head or walk around while listening to a fixed sound source; quite
obviously, our brain is self-trained to ignore/compensate for this
kind of "problems" as far as they fall into what it recognize as a 
"normal" range).

On the other end, the effect of clock jitter on digital audio is a 
completely different thing.

It does not globally (and, in a sense, "linearly") alter the "pitch" 
of the sound as analogue W&F does; rather, in the digital domain the 
jitter deeply affect the A/D and D/A conversion mechanisms, causing 
wrong recording and/or reconstruction of the analogue waveforms.

Let' try to visualize what happens.

When we do an A/D convertion, we take a "sample" of the original 
analogue signal every some predefined time interval "T", and store 
the corresponding amplitude as a number (value).

When we do D/A, basically what we do is to take all those values 
and "set them out" one after the other at the very same rate (time
intervals) that we have used in the A/D process.

The theory behind the process guarantees us that - as far as 
we limit the bandwidth of our signals to less than half of the 
sampling rate - we can reconstruct the original waveform.

But what happen if the clock used for A/D is different from the
one used for D/A? (as it always happens to some extent, BTW).

Well, if there is a constant difference in the two clock rates
(i.e., frequencies), what we get is that the samples got either 
"squeezed" or "draw apart"; the resulting effect is somewhat 
similar to that of a difference between recording and playback 
speed on analogue tapes or disks... the "pitch" get altered.

Should we use a really bad, unstable clock source for either 
A/D and/or D/A conversion, we would also get pitch alterations 
(fluctuations) effects similar to analogue W&F. 

Yet crystal clock oscillators used for digital audio are in fact 
quite stable and normally this "digital W&F" effect is practically 
negligible.

But what happens if we have small, "microscopic", differences in 
the time intervals between each sample and the following one, that 
is jitter?

One may be tempted to answer: "well, likely a microscopic - thus 
insignificant - W&F like effect". 

Unfortunately, it's not so. Not at all.

An analogue signal is a continuous wave which assume a different
"value" (amplitude) for each given time "t".

When we do A/D, we takes samples of that wave at the times t, t+T, 
t+2T, t+3T, etc...

if we have jitter, "T" is no longer a constant, but becomes T+dt, 
where the jitter term "dt" may be either positive or negative and
in general is of a "random" nature.

This means that we are taking samples at the wrong times - that is,
we are storing the wrong values!

(think about it: unless we are sampling a constant amplitude, that 
is a DC offset, in general on the original waveform different times 
corresponds to different values...)

Similarly, if we have jitter when we do D/A, we set out the "right" 
samples at the wrong times - which is the same as setting out wrong 
values at the "right" times!

(again, think about it: even if we have the "right" sample values, 
at any time different from exactly "what it should be", the original 
waveform would have had assumed some different values...).

That is, clock jitter "translates" into amplitude errors, causing
(non-linear) distorsions!

(and of the worst kind too, as they are in fact somewhat similar to 
those caused by the infamous "cross-over" distorsion of amplifiers)

That's why, in short, even tiny, apparently insignificant amounts 
of jitter actually translates into well audible audio "defects".

[what's worse is that, unfortunately, these kind of defects are 
usually much more "unpleasant" to our ears (thus more annoying)
than, say, small amounts of "W&F" of the analogue era... :-(  ]

Of course, the whole story is much more complicated than this brief 
explanation... different DAC technologies, oversampling, resampling, 
digital & analogue filtering, etc. all changes the details of jitter 
interactions and effects.

Moreover, it also matter a lot whether the jitter is "purely random" 
or somehow correlated to the signal, as it happens e.g. when the DAC 
clock is reconstructed from an S/PDIF stream, or when either analogue 
or digital signals finds their ways into some ground or power supply 
lines (-> modulating the clock), etc.

(as it turns out from tests done, correlated jitter seems to be the 
worst one for the perceived sound quality... what a luck!).


In conclusion, from now on, when someone from a marketing department 
will tell you once again about the "perfection and purity of digital 
audio"... don't believe 'em anymore!

Digital audio is by no means perfect. It may not have the old, well 
known problems of the analogue systems (at least some of them), but 
it does have many new problems on its own.


(hope it helps... and sorry for bothering those who knew it well).


Ciao,
                                Paolo.

--
Skype: Paolo.Saggese
http://borex.lngs.infn.it/saggese
You can still escape from the GATES of hell: Use Linux!

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