On 7/23/15 1:12 AM, Peter S wrote:
On 23/07/2015, robert bristow-johnson<r...@audioimagination.com> wrote:
okay, since there is no processing, just passing the signal from A/D to
D/A converter, there is only one quantization operation, at the A/D. if
it's an old-fashioned "conventional" A/D, the quantization operation is,
essentially, a non-linear staircase operation and the error is a
measurable and then predictable function of the input. if it's "properly
dithered", the error will be well described as "noise" that's white with
DC=0 and AC power decoupled from the input value. with noise-shaping,
the noise wouldn't have to be white, but the AC power level would
increase. sigma-delta (Σ-Δ or Δ-Σ) converters might have a similar
signal+noise model. that's N1.
Let me point out to some very important detail that you've just missed
- I was not talking about quantization noise at *all*. I implied that
in the clause "among other noises", without giving any detail about
quantization noise _whatsover_.
well, then you're missing something. that's the main "noise". if it
ain't, then the hardware design is dirty.
and what i was "missing" is semiconductor noise or whatever crap we get
from dirty power supplies and the like. i am leaving that to the
circuit designer and layout designer.
if one is trying to model the A/D and D/A as a wire, and trying to
subtract the input from the output to see the error, while delay might
be something to worry about, semiconductor noise is *not* what i would
worry about. if i had to worry about it, there is something else deeply
wrong in the hardware circuit.
I was talking about the noise _floor_,
which is a remarkably different type of noise.
<sigh>
If you have any converter and plug in some cable, without any actual
input/output,
you mean an open circuit on the other end of the cable?
what you'll measure is *noise* (both on the ADC and the DAC).
well, there's hum and there's noise. not the same thing.
if the hum, due to a floating open circuit, isn't bad then the major
component of noise you should be seeing is the actual quantization noise
of the A/D and if the D/A is also sigma delta, there is another noise
source there. and this noise has a numerical root.
I was talking about _that_ (noise floor), not the noise from the
quantization.
better look up sigma-delta converters.
Yes, there's *also* quantization noise, which I was not
even mentioning at all, so it's not in the formulas that I wrote,
which would be:
S + N1 + Q1 + N2 + Q2
where Q1 and Q2 are the _quantization_ noise from the ADC and DAC, and
N1/N2 are the noise from the noise _floor_ of the ADC and DAC.
more of the noise _floor_ of A/D and D/A converters comes from numerical
operation of these "1-bit" converters that from noisy analog front end
or back end.
there *is* error at the D/A, due to non-linearity, but i wouldn't call
that noise.
There is _definitely_ a noise floor. Which is, pretty much just noise.
If you record the input of your 24 bit sound card without plugging in
*anything*, you pretty much get just noise (whatever exact
distribution, possibly depending on the noise shaping of the converter
and other factors).
and it's a function of the input.
The noise floor is definitely NOT a function of the input.
the error due to non-linearity of the A/D is a function of the input.
the noise floor, due to an open circuit, might include hum, because your
open circuit cable might be a little antenna.
if it's a quiet short-circuited input, if the noise from the analog
front end exceeds the noise from the converters, some might say that the
front end needs attention.
Even if you
have no input at all (= you plug in _nothing_), you *will* get noise
in the lowest bits of a 24-bit converter. *Irregardless* of the input.
the last statement you made is inconsistent with the "no input at all"
statement.
Even using the most high-end sound cards. The lowest 3-4 bits will
*always* be noise. Feel free to test this experimentally, if you doubt
my words.... If there's *no* noise floor, then why don't we have
32-bit converters with near 192 dB dynamic range?
one reason is that we cannot make parts with the tolerances necessary.
According to what
you say, just apply some noise shaping, and "voila! ~192 dB dynamic
range!" Yet that doesn't happen.
if the required bandwidth of the input is low enough, yes you can. if
you want to measure DC (if you don't have a blocking cap and your A/D
can handle DC), you can with averaging, get to very high S/N for just DC
and the few Hz (or tenths of Hz) around 0. since pure DC has a very low
bandwidth, an arbitrarily low bandwidth, you can widen the window of
averaging to as wide as necessary and get 192 dB S/N.
In order to be able to "fix" that
noise, you'd need to be able to "predict" that noise.
or make use of the statistics of that noise (known in advance).
You cannot use the statistics of the noise floor to "fix" (=
eliminate) that noise. No matter how many statistics papers you read,
that won't work. If it was "fixable", then please tell me, why do even
the best, most expensive, $3000 sound cards will have just noise in
the lowest bits? Tell me. If that were possible, then those zillions
of dollars spent on converter research, should have been enough to
figure it out, don't you think? Or you know something that _all_ sound
card manufacturers don't know?
no, i just know something about oversampling.
but if the noise
is colored (and you know about the spectrum) and if the noise has a
p.d.f. that is not uniform, you can make guesses about where the next
sample is that are better than wild-assed guesses.
Yet you cannot "fix" it (=eliminate it). Yes you may improve it
_slightly_ with noise shaping (so you push it into bands where
psychoacoustically it may sound like less noise to the human ear), but
that won't "eliminate" it.
to what degree you reduce noise depends on the bandwidth of interest of
your signal and the sampling rate of the A/D and D/A.
Sorry that's impossible. No matter how many
degrees you have and how many thousand hours you spend in the library,
that just won't work. And even if that gives you psychoacoustically
better noise profile, that won't "fool" a measurement equipment (which
is unaffected by psychoacoustics, unless it's deliberately built in
via some weighting curve.)
<sigh>
And there's no magic alien technology that will eliminate the noise
_floor_ of a converter, and magically give you 32-bit 192 dB dynamic
range. No such converter exists. Why don't 24-bit converters have 144
dB dynamic range? Answer: "noise floor".
do you understand the sources of that "noise floor"?
exactly what audio codecs are you using? if they're sigma-delta (which
are, now-a-daze, nearly ubiquitous in audio), the major component of the
"noise floor" is actually from the operation of the converter and has a
numerical root. that is louder than the noise from the analog front
end, unless your analog front end is particularly noisy. some folks
design front ends that are quiet enough that the converter people
actually ask for a noisier front end so that their A/D has its input
tickled more (which makes it toggle bits).
Peter, if you can take or sit-in some grad courses, i might recommend a
course in Statistical Communications or at least a course in Random or
Stochastic Processes. there is ostensibly some stuff you're missing here.
Robert, your constant consdecending is starting to get really boring.
Earlier you told me to "not become patronizing",
plonk. you and Theo can slug it out. just patronize each other. leave
the rest of us out. i'll stop reading the posts.
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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