# [time-nuts] from Sputnik to CD

Tom Van Baak tvb at LeapSecond.com
Mon Oct 8 16:24:02 EDT 2007

```> As one who has worked in the pro digital audio field for years, I can
> tell you that sub-100 ps jitter very definitely can be heard,
> depending on its spectrum.  Modern sigma-delta ADCs and DACs use
> oversampling clocks of 12 to 50 MHz for sample rates of 44.1 kHz to
> 192 kHz at 24-bit resolution and achieve SNR and DNR of 120 dB or
> better, integrated over the audio range.  The noise floor can be -144
> dB or better and a 1-bit signal can be discerned.  Higher-end
> consumer gear do use these as well as pro equipment.

Can you show us the math behind this?

If I calculate 1 / 192 kHz / 2^24 = 0.3 ps, my crude intuition
says that at 192 kHz (~ 5 us) one ps of time jitter is roughly
equivalent to about 2 bits of noise on a 24-bit DAC, yes?

Similarly for a vintage 16-bit DAC at a modest 44.1 kHz, one
bit of DAC noise is equivalent to ~300 ps of time jitter (using
a calculation of 1 / 44.1kHz / 2^16 = 346 ps).

Is this the right way to do the math? Am I even close?

It seems to me that all short-term imperfections in timebase
stability have the identical effect as short-term imperfections
in DAC stability and is also related to the number of bits of
resolution in each sample.

So debates about signal fidelity, which are often framed in
terms of sample rate (e.g., 44.1 vs. 192 kHz) or sample width
(e.g., 16 bits vs. 24 bits), should equally discuss clock jitter
parameters, no? Only, I rarely see much about the role of
clock jitter in digital audio, or if I do, it's handwaving instead
of real data.

I don't want to get that far off time-nuts topics, but this does
seem to be an interesting real-world application of precise
time and I've not run across a scientific treatment of it, one
that includes real performance measurements of various
digital audio recording and playing devices, etc.

It's also interesting when two list members disagree by so
many tens of dB, so I'm hoping David and PHK can settle
this for us.

/tvb

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