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On 27 Jul 2004 23:57:24 GMT, Kurt <kurt_fonseca@hotmail.com> wrote:

>As I see it, averaging the 64-plus samples which follow a non-linear

>curve (amplitude versus time is non-linear in audio signals) will

>yield a sampling value, but that sampling value will not correspond

>to the instantaneous value at the exact midpoint of the time range --

>it will reflect some value away from the exact midpoint in time. This

>then leads to an error. How much the error is depends upon the

>delta-t represented by the averaged samples and now close to linear

>the amplitude is in that delta-t. (Looking at this another way, an

>"average" is not necessarily the same as a "mean", e.g., let's

>determine the amplitude of the crest of a sine wave using this

>n-samples over delta-t on both sides of the crest.)

Sounds convincing intuitively, but you'd need to find someone with

better maths than mine to prove the point, since in practice it *does*

work, and high-oversampling converters can be shown to have

vanishingly low error levels in the top octave, where you'd expect

such problems to be very obvious.

>The other question is why the need for high-oversampling anyway? If

>it is possible to nearly instantaneously sample at any point, why

>not just use that value corresponding to the final sampling time?

>Or is this oversampling done to minimize random hardware errors?

It is indeed done to minimise random hardware errors. Basically, we

can measure time *much* more accurately than we can measure amplitude,

so a 5-bit converter (only needs to be 5% accurate) oversampled x64

and noise-shaped back to 20-bit resolution in the audio band, is

significantly more accurate than a straight 20-bit converter (needs to

be 0.0001% accurate!) can ever be.

>The last question: Is there a spec which, for any ADC device, gives

>an estimate of the error of sampling (besides quantization error)

>based on the various real-world effects in trying to determine the

>instantaneous amplitude of a signal at any moment in time?

You can certainly measure its non-linearity and monotonicity.

> In

>addition to the linear/non-linear averaging (as noted above), there

>are no doubt other sources of error (e.g., the sample-and-hold

>capacitor, during charging, cannot exactly follow the voltage --

>there is a small lag there.)

Yes, that is still the bane of professional engineers in the

measurement field, but high-oversampled single-bit converters have

much less of a problem with pedestal voltage, and it's not such a big

deal anyway with AC signals.

> I find this "faith" that ADC will

>determine the exact value (within bit-roundoff-error) of a signal at

>any instant of time to be somewhat troubling.

It's not a matter of faith - these devices do get *tested* when

they're being developed, y'know!

>If the designers of ADC

>considered all the sources of errors and minimized them by clever

>design to be below the bit-roundoff-error (quantization error), then I

>have no difficulty.

They do - that's what they get paid for. Note however that you can't

achieve a full 24-bit dynamic range, due to thermal noise. Devices

such as the dCS RingDAC can however be shown to have true 24-bit

*linearity* by using narrow-band measurements.

> But in what I've heard so far, I do not get warm

>fuzzies that anyone here knows for sure that professional-grade ADCs

>get the sampling error due to circuit design below that of the

>unavoidable bit-roundoff-error.

Ask the technical departments of Prism Sound, Apogee and dCS. These

guys are generally very forthcoming about technical details.

> How do we know that a sample which

>should be +123456 (when rounded off, assuming 24-bit here) will not be

>sampled instead as +123458 due to these various real-world hardware

>errors?

We measure it...........................

BTW, I'd be surprised if *any* real-world 21st century audio ADC was

only 16-bit accurate, as you imply above. Most can achieve 18-19 bit

accuracy with ease - which is more than enough for audio.

>Again, just playing Devil's Advocate here.

Does no harm to check these things!

--

Stewart Pinkerton | Music is Art - Audio is Engineering