# Reference on quantization noise modeling

Started by December 8, 2008
```Does anyone know some examples where quantization is modeled by a linear
model as follows:
y = Q(x),
modeled as
y = a*x + q,
where q is an additive noise, preferably white Gaussian.
See the following paper for an example:

Fletcher, A.; Rangan, S.; Goyal, V. & Ramchandran, K. Robust Predictive
Quantization: Analysis and Design Via Convex Optimization Selected Topics
in Signal Processing, IEEE Journal of, 2007, 1, 618-632

I am trying to find other examples of the use of this kind of quantizer
model.
Best regards,

Thomas Arildsen
--
All email to sender address is lost.
My real adress is at arildsen dot org for user thomas.
```
```On 8 Des, 12:11, Thomas Arildsen <tha.es-aau...@spamgourmet.com>
wrote:
> Does anyone know some examples where quantization is modeled by a linear
> model as follows:
> &#2013266080; y = Q(x),
> modeled as
> &#2013266080; y = a*x + q,
> where q is an additive noise, preferably white Gaussian.

It's been 15 years since I last looked up these things, but
I'm pretty sure I saw it done like this in the book by
Gersho & Gray:

http://www.amazon.com/Quantization-Compression-Springer-International-Engineering/dp/0792391810/ref=sr_1_1?ie=UTF8&s=books&qid=1228735331&sr=8-1

Check out this or similar books in your local library.

Rune
```
```On Mon, 08 Dec 2008 03:26:28 -0800, Rune Allnor wrote:

> On 8 Des, 12:11, Thomas Arildsen <tha.es-aau...@spamgourmet.com> wrote:
>> Does anyone know some examples where quantization is modeled by a
>> linear model as follows:
>> &nbsp; y = Q(x),
>> modeled as
>> &nbsp; y = a*x + q,
>> where q is an additive noise, preferably white Gaussian.
>
> It's been 15 years since I last looked up these things, but I'm pretty
> sure I saw it done like this in the book by Gersho & Gray:
>
> http://www.amazon.com/Quantization-Compression-Springer-International-
Engineering/dp/0792391810/ref=sr_1_1?ie=UTF8&s=books&qid=1228735331&sr=8-1
>
> Check out this or similar books in your local library.
>
> Rune

Thanks. I have Gersho & Gray. I am flipping through just now. What I can
find is the "Additive Noise Model of Quantization" on pp. 148-150.
However, they do not seem to mention the gain part of the model I am
considering...

Thomas Arildsen
--
All email to sender address is lost.
My real adress is at arildsen dot org for user thomas.
```
```On Mon, 08 Dec 2008 11:11:04 +0000, Thomas Arildsen wrote:

> Does anyone know some examples where quantization is modeled by a linear
> model as follows:
>   y = Q(x),
> modeled as
>   y = a*x + q,
> where q is an additive noise, preferably white Gaussian. See the
> following paper for an example:
>
> Fletcher, A.; Rangan, S.; Goyal, V. & Ramchandran, K. Robust Predictive
> Quantization: Analysis and Design Via Convex Optimization Selected
> Topics in Signal Processing, IEEE Journal of, 2007, 1, 618-632
>
> I am trying to find other examples of the use of this kind of quantizer
> model.
> Best regards,
>
> Thomas Arildsen

It turns out that good old Jayant & Noll have a description of the model:

Jayant, N. S. & Noll, P. Digital Coding of Waveforms - Principles and
Applications to Speech and Video Prentice Hall, 1984

Thomas Arildsen
--
All email to sender address is lost.
My real adress is at arildsen dot org for user thomas.
```
```Thomas Arildsen <tha.es-aau-dk@spamgourmet.com> writes:
> [...]
> However, they do not seem to mention the gain part of the model I am
> considering...

Just move the gain ahead of the quantizer into its own block:

x -> a*x -> q(a*x)

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```