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_. I was talking about the noise _floor_,
which is a remarkably different type of noise.
If you have any converter and plug in some cable, without any actual
input/output, what you'll measure is *noise* (both on the ADC and the
DAC). I was talking about _that_ (noise floor), not the noise from the
quantization. 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.
> 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. 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.
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? According to what
you say, just apply some noise shaping, and "voila! ~192 dB dynamic
range!" Yet that doesn't happen.
>> 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?
> 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. 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.)
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".
> 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", yet now you do this
condescending behaviour (even without understanding what I say, and
sorry to point out, but also having invalid assumptions - tell me,
have you ever tried to record something with no input using a 24-bit
converter? Have you ever looked what you have at the lowest bits? Do
you understand what the term "noise floor" means?).
And by the way, yes, I know about noise shaping and sigma-delta
converters (we can discuss that topic if you prefer, I like that
topic), yet I was not talking about that, but rather, the noise
_floor_ of a converter. Which is pretty much *always* there,
irregardless of the input/output. If you don't think there's a noise
floor, then there's "ostensibly some stuff you're missing here".
> depends on what we have available for sample rates. essentially we are
> only limited by the laws in Information Theory. if i have a 192 kHz
> system and i only need to measure a 30 Hz waveform, there is a lot i can
> do to mitigate noise.
Let me point out to another very important point that you missed: Theo
was trying to apply some *digital* filtering before the reconstruction
to get a better reading on the output. Now, that certainly won't help
you much if you want to output say, a 30 Hz sine wave - the DAC will
add its own noise of whatever distribution, irregardless whatever you
do to the digital signal.
Yes, you can - trivially - apply a 30 Hz very narrow bandpass filter
on the *analog* output of your DAC to separate your 30 Hz sine wave
from the noise of the DAC, except the situation to be considered was
something else (doing digital filtering *before* the DAC). So that's
two markedly different situations, which should not be confused.
Yes, trivially if you take a sine wave, add (whatever) noise, and then
you use a very narrow bandpass filter tuned to the frequency of the
sine wave, then you (pretty much) get back you original sine wave, and
filter out the noise. So what? That won't help Theo with his digital
voodoo.
(Note: a narrowband resonant filter with zero bandwith (= infinite Q)
is *precisely* a self-oscillating sine-wave generator. So yes,
trivially, the output of a sine wave generator, is a sine wave.)
> they're doing it. it's called "noise shaping" or "error shaping". it's
> how we mitigate the huge quantization error of a 1-bit converter and
> make it sound like a 20-bit converter, and a linear one at that.
Exactly. Hence, noise shaping or error shaping is already built into
your sound card. There's no digital voodoo you can make before the DAC
to improve that further. Have you even read and tried to understand
what Theo's trying to do?
> that's just not always true. it depends on what you know about the
> signal you're after. if it's not broad-banded, there *are* things you
> can do about the noise getting added to it.
Yes, *if* you apply filtering on the analog output. Which was *not*
what Theo was trying to do, if I understand what he wrote. Also note
that he was trying to apply this to a broadband saw wave, not a
narrow-band signal. Hence, there *aren't* (too many) things you can do
about the noise getting added to it. Your argument sounds like a
strawman argument.
- Peter
--
dupswapdrop -- the music-dsp mailing list and website:
subscription info, FAQ, source code archive, list archive, book reviews, dsp
links
http://music.columbia.edu/cmc/music-dsp
http://music.columbia.edu/mailman/listinfo/music-dsp
