Re: To RAW or not to RAW?

Floyd Davidson wrote:
[]
> Nobody cares if you *believe* one term is better. The fact is
> that there is a standard definition, and you are using the wrong
> criteria to come to the wrong conclusions, partially because you
> don't understand or use proper terminology.
>
> And then you have the nerve to claim I'm either wrong or using
> improper terminology. Note that I've been citing multiple
> references, and you have yet to provide even a single reference
> that agrees with you instead of me.

The term quantisation noise is so widely used, but if you insist:

http://www.digitalradiotech.co.uk/sampling.htm

>>>> If modelled as a gaussian white noise,
>>>
>>> Do you understand what "bandwidth limited" means, when
>>> referenced to a channel?
>>
>> Yes. Quantisation error depends on the signal level, and not its
>> bandwidth.
>
> Ahhh... you don't have a clue as to what the term means.

I will let others be the judge of that!

> It merely means that the *channel* does not have unlimited
> bandwidth. For example, a typical voice channel used in the
> telephone industry is thought of as a 4KHz wide channel. In
> fact it is bandwidth limited by filters at the transmit end, and
> is more like 3.75 KHz wide. Of course with a Nyquist limit of 4
> KHz, that is significant because aliasing (ouch, another linear
> distortion!) is filtered out and right along with it a great
> deal of the distortion products from quantization. The
> amplitude distortion (ouch, another linear distortion) that
> results is out of the range necessary for use by the human ear,
> but does affect V.34 and V.90 modems. The phase distortion
> produced (ouch again, yet *another* linear distortion) is of no
> consequence at all to human ears, but again it affects modems.

Quantisation error has nothing to do with bandwidth. It exists because
whilst an analog signal has a continuous range, the digitised signal is
only represented by a finite set of values.

> Regardless, quantization error, as I previously noted, is
> typically modeled as an additive white Gaussian noise (AWGN).
>
> That is *not* to say that quantization error is Gaussian. "One
> reason for this is that a Gaussian distribution is approached
> when a large number of random processes with identical
> distributions combine to produce a cumulative effect -- even if
> the individual processes are not themselves Gaussian." Bissell
> and Chappman, "Digital Signal Transmission", 1992, Cambridge
> University Press, p 68.

This may be true where there are a large number of similar amplitude
values, but it is not true where there is a single dominant noise source.

[]
>> Yes, I understand the Gaussian distribution. Quantisation noise
>> does not have a Gaussina distribution, but a linear distribution.
>
> It is neither. Whatever gives you the idea that it is linear?
> For linear sampling, the error is necessarily significantly larger
> for small signals than it is for large signals.

The amplitude distribution is linear (assuming an ideal ADC). The
magnitude of the error is the same for both small and large signals. Of
course, that means that is the signal amplitude is reduced, the amplitude
of the noise will increase relative to the signal. Note that this is in
complete contrast to harmonic distortion in analog systems, where the
amplitude of the distortion reduces as a fraction of the signal amplitude
when the signal level is lowered. This distinction is another reason
practitioners prefer the term noise.

[]
>> I did not say that quantisation error was linear - but that it has a
>> linear distribution (ranging from minus one half to plus one half of
>> the quantising steps).
>
> Which of course means that it does *not* have a linear
> distribution, unless you adjust the sampling steps to match the
> signal level.

We have been talking about analog signals which are digitised to 12-bit
accuracy. The signal level is some 4096 times the step size.


> I noted right at the start that many people use the term noise,
> and that it is technically incorrect. That is *obviously* true.
> Claiming it is "best described as noise" is simply ignorant. It
> may work to use that term, but it is far from "best".
>
> That is *not* to say that many rather good sources do not
> intermix them. But if you find a discussion of the technical
> difference between distortion and noise, *every* *single* *one*
> will point out that quantization causes distortion, not noise.

Many people use the term noise because it is the most useful way to model
the effects of quantisation within a system, as you have already quoted.
As distortion can be used to describe so many different errors, I would
use the term linearity error to describe quantisation error if you forced
me to name an alternative.

David


.

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