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Started by Alexl August 17, 2009
Hi,
What is the form of Quantization Noise as a function of time?

A.L. 


"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.
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
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 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

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
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
>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.