>How can QN be pure stochastic process if we know how it changed with
respect
>to time, 

As Vlad pointed out, it's not really a stochastic process.  However, Tim
explained the times when it's okay to treat it as one.  The most physical
explanation is as a nonlinear I/O block of some sort, but symbolic math is
often intractable when you treat it that way, so you want situations where
you can approximate.

It may or may not be useful for your app (which is?), but for any given
signal realization (almost always by simulation), you can find the form of
the quantization noise by emulating the behavior of your ADC and
subtracting the original signal.  Doing this many times for different
realizations of your input signal (or different ADC dice, within mfg
variations!), assuming your input signal is not perfectly deterministic,
will usually (unless the quantization is horrible) yield a different result
each time, and, if those "residuals" are white, or a reasonable
approximation thereof, you might be able to treat it as AWGN.  Trying this
out for your signal will give you more intuition.  Or you can take Tim's
"Murphy's Law" approach, outlined above.


> and  we can not decrease it by averaging as usual noise.

Sometimes you can.  Why do you say that?  To give a trivial example, if
you have a constant input, corrupted by some noise, you will see variation
over a few LSbits, say.  If you average, you will generally get a better
estimate than a point sample.  It is difficult to give a general approach,
however.

Yes ,we see the deterministic function on Fig 2 in the
http://www.lr.ttu.ee/irm/sideseadmete_mudeldamine/AD_MT_Tutorial.pdf.
How can QN be pure stochastic process if we know how it changed with respect
to time, and  we can not decrease it by averaging as usual noise.

"Vladimir Vassilevsky" <nospam@nowhere.com> wrote in message 
news:eoGdndQlZ-XrBxTXnZ2dnUVZ_gqdnZ2d@giganews.com...
>
>
> Alexl wrote:
>
>> Hi,
>> What is the form of Quantization Noise as a function of time?
>
> What is commonly referred as the "quantization noise" is actually a 
> combination of the static nonlinear distortion and aliasing. This is a 
> deterministic process; the notion of the "quantization noise" is just an 
> oversimplification to get to the coarse estimates.
>
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultant
> http://www.abvolt.com

Alexl wrote:

> Hi,
> What is the form of Quantization Noise as a function of time?

What is commonly referred as the "quantization noise" is actually a 
combination of the static nonlinear distortion and aliasing. This is a 
deterministic process; the notion of the "quantization noise" is just an 
oversimplification to get to the coarse estimates.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Mon, 17 Aug 2009 10:38:40 -0500, Tim Wescott wrote:

> On Mon, 17 Aug 2009 09:51:46 +0300, Alexl wrote:
> 
>> Hi,
>> What is the form of Quantization Noise as a function of time?
>> 
>> A.L.
> 
> Entirely signal dependent.  For an ADC that's dominated by quantization
> noise it'll depend on the parent signal, with a more slowly varying
> input signal making for a more slowly varying quantization noise.  For
> an ADC that's dominated by wideband random noise (most monolithic ADC's
> that have high bit counts for their speeds, like 100ksps 16-bitters,
> 60Msps 14- bitters, etc., show several counts RMS of Gaussian wideband
> noise) it'll just be another source of white noise contributing to the
> total.

When I want to evaluate the impact of quantization noise on a system I 
first ask if the signal has enough content to swamp out the time behavior 
of the quantization (i.e. is there enough noise or variation in the 
signal that the quantization noise is spread out).  If the answer is "no" 
or "I can't tell" then I assume that the quantization noise will be 
concentrated at the absolute worst possible frequency (usually DC or the 
resonant frequency of some 2nd-order filter).  If the noise is too much 
at that one frequency, then I redesign or I _carefully_ evaluate my 
assumptions to see if I can validly assume white quantization noise.

-- 
www.wescottdesign.com

On Mon, 17 Aug 2009 09:51:46 +0300, Alexl wrote:

> Hi,
> What is the form of Quantization Noise as a function of time?
> 
> A.L.

Entirely signal dependent.  For an ADC that's dominated by quantization 
noise it'll depend on the parent signal, with a more slowly varying input 
signal making for a more slowly varying quantization noise.  For an ADC 
that's dominated by wideband random noise (most monolithic ADC's that 
have high bit counts for their speeds, like 100ksps 16-bitters, 60Msps 14-
bitters, etc., show several counts RMS of Gaussian wideband noise) it'll 
just be another source of white noise contributing to the total.

-- 
www.wescottdesign.com

On Mon, 17 Aug 2009 09:04:55 +0100, Phil O. Sopher wrote:

> "Alexl" <alexl@chem.ch.huji.ac.il> wrote in message
> news:h6aum3$3ue$1@news.iucc.ac.il...
>> What is the form of Quantization Noise as a function of time?
> 
> Except for a few special cases (eg, your input signal is a fixed DC
> level in which case you will have a quantization error as opposed to a
> noise function) then there is no answer to the question in the way that
> your question implies (at least to me)
> 
> Quantization noise is a statistical function, with a linear distribution
> from 0-
> (zero minus)  down to the minimum quanization step size.
>
> The noise signal is always negative because the effect of quantization
> is to round down the quantized value.
> 
> The smaller limit is 0- because an input signal EXACTLY at the
> quantization boundary will always be correct, with no added noise.

Depending on your signal processing, quantization may round instead of 
truncating.  Often if the quantization is happening in the digital domain 
someone will take the trouble to round the output.

Also depending on your signal processing, the bias from quantization 
noise may be swamped by other biases.  This is often the case when using 
an ADC -- most ADCs have far worse bias specs than any other source of 
error, so errors of several counts, or even several tens of counts, is 
not uncommon.

So I usually end up modeling quantization as rounding, with a bias stuck 
in there as appropriate.  But that doesn't change the fundamental nature 
of the thing, which is a uniformly-distributed error around the 'correct' 
value.

-- 
www.wescottdesign.com

"Alexl" <alexl@chem.ch.huji.ac.il> wrote in message 
news:h6aum3$3ue$1@news.iucc.ac.il...
> What is the form of Quantization Noise as a function of time?

Except for a few special cases (eg, your input signal is a fixed DC level
in which case you will have a quantization error as opposed to a noise
function) then there is no answer to the question in the way that your
question implies (at least to me)

Quantization noise is a statistical function, with a linear distribution 
from 0-
(zero minus)  down to the minimum quanization step size.

The noise signal is always negative because the effect of quantization is
to round down the quantized value.

The smaller limit is 0- because an input signal EXACTLY at the quantization
boundary will always be correct, with no added noise.