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?

# The optimal quantization

Started by ●May 22, 2012

Reply by ●May 22, 20122012-05-22

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."

Reply by ●May 22, 20122012-05-22

>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.

Reply by ●May 22, 20122012-05-22

"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.See also "rate distortion theory." -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com