# The optimal quantization

Started by May 22, 2012
```Hi,
Anybody knows who and where works in optimal quantization area?  Max Lloyd
quantizer was created 50 years ago. What is going on this scientific
direction now?

```
```On 5/22/12 12:47 AM, st256 wrote:
> Hi,
> Anybody knows who and where works in optimal quantization area?  Max Lloyd
> quantizer was created 50 years ago. What is going on this scientific
> direction now?
>

how do you mean "optimal"?  a non-uniform quantizer?  companding?

or optimal regarding error shaping (a.k.a. "noise shaping")?

pre/de-emphasis?

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```>how do you mean "optimal"?  a non-uniform quantizer?  companding?
>
>or optimal regarding error shaping (a.k.a. "noise shaping")?
>
>pre/de-emphasis?
>

OK, I'll try to describe the theme more in detail.
When we do analog processing so we work with L2 space.  Note, number of
this space vectors are infinitive. If we do digital processing then we work
in finite set. Note, number of this space vectors is finite. Procedure
mapping L2 to finite set is named as quantization.

After quantization we have some distortion. If there is a criterion then it
is possible to minimize the distortion during quantization.  For example,
Max Lloyd quantization minimizes a mean square of error by changing
quantization levels during quantization of independent stochastic values.

As you see, the main problem for optimal quantization is splitting of L2
space to finite number of subspaces optimally according some criterion. For
example, according criterion of minimum of mean square error.

```
```"st256" <st256@n_o_s_p_a_m.mail.ru> writes:

>>how do you mean "optimal"?  a non-uniform quantizer?  companding?
>>
>>or optimal regarding error shaping (a.k.a. "noise shaping")?
>>
>>pre/de-emphasis?
>>
>
> OK, I'll try to describe the theme more in detail.
> When we do analog processing so we work with L2 space.  Note, number of
> this space vectors are infinitive. If we do digital processing then we work
> in finite set. Note, number of this space vectors is finite. Procedure
> mapping L2 to finite set is named as quantization.
>
> After quantization we have some distortion. If there is a criterion then it
> is possible to minimize the distortion during quantization.  For example,
> Max Lloyd quantization minimizes a mean square of error by changing
> quantization levels during quantization of independent stochastic values.
>
>
> As you see, the main problem for optimal quantization is splitting of L2
> space to finite number of subspaces optimally according some criterion. For
> example, according criterion of minimum of mean square error.