In article , Carey
Carlan wrote:

Jay - atldigi wrote in
:

But that's exactly my point: only the -100 component is what you've
gained. The -1 component is not rendered any better than it was
before.

First up, don't get hung up on this -1 and -100 example that was just in
reponse to another post where the example was given. The original
thought was useful enough conceptually, but shouldn't be thought of as a
real world practical example.


Jay, as I am a person steeped in computer bits but weak on audio theory,
I ask you to explain that statement.

A 24-bit signal offers +/- 8,388,608 possible volume levels.

A 16-bit signal supports only +/- 32,768 volume levels.

Only +/- 128 levels (48 dB) of the 24-bit signal are less than the lowest
bit of the 16-bit (providing lower threshold).

The other bits provide 256 more possible levels between each of the 16-
bits' levels.

Do you disagree with any of the above? It's just math.

Is your argument that this higher precision is inaudible?

That's the basic math for an ideal quantizer which is not what we use in
audio. Ideal (noiseless) quantizers are an excellent and necessary
learning aid, but aren't the ultimate implimentation we use in our audio
ADCs as they are non-linear and cause distortion (this non-linear
behavior being what you guys are giving examples of and worrying about).
When you look at a digital audio system as a whole, not just the
isolated parts (quantizer, sampler, filter etc.), it actually behaves a
little differently from how it's isolated parts first look on paper. We
deliberately use non-ideal quantizers to achieve linearity.

The key here, and some might not want to hear it, is dither. Dither is
not only used in the familiar requantizing. An example of requantizing
would be when you have a 24 bit file on your computer and "dither it"
down to 16 bits to go on a CD. In digital audio, all quantizers need to
be dithered. The quantizer in your ADC needs to be dithered to behave
properly.

Here's the important sentence taken right from Watkinson:

"The dither has resulted in a form of duty cycle modulation and the
resolution of the system has been extended indefinitely instead of being
limited by the size of the steps."

To explain all of this fully, the post would get very, very long. It may
be more effiecient to order a few AES papers (I could offer appropriate
references) and get Watkinson's and Pohlmann's books. However, I can
offer a few points that may be helpful.

The transfer function really does become linear with dither, at the
expense of a noise floor. Even in an ideal (noiseless) quantizer, loud,
complex signals' quantizing error will manifest as random noise. The
numerical values for the samples in such audio are so widely varying
that the quantizing errors will be independent or each other and will
distribute themselves in such a random pattern according to probability
that it will essentially behave as broadband noise (yet not of the same
gaussian distribution as thermal noise in an analog circuit).

Smaller or less complex signals, however, are more of a problem. This is
where the error becomes correlated to the signal and you get distortion.
What's worse, the distortion happens after the anti-aliasing filter, and
the harmonics of the distortion above Nyquist will alias causing
"birdies". Correct application of dither decorrelates the quantizing
error and linearizes the transfer function at the expense of a noise
floor. The resolution becomes, in effect, infinite. The limitation is
that the noise floor can be plainly audible in low resolution systems
and obscure low level detail in addition to being distracting. However,
within it's available dynamic range, the system is infinite. You can't
get better than that, even if you throw more bits at it. Taken as a
whole, the system works better than it would appear from the initial
learning aid of the ideal quantizer on paper. Add more bits, the noise
floor drops, and you can resolve smaller (quieter) details.

--
Jay Frigoletto
Mastersuite
Los Angeles
promastering.com