Re: how to find the best ADC step size?

From: Clay S. Turner (Physics_at_Bellsouth.net)
Date: 12/22/04 

Date: Wed, 22 Dec 2004 09:47:00 -0500

Hello Randy,
comments below:

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxppt12cy6f.fsf@usrts005.corpusers.net...
> "Clay S. Turner" <Physics@Bellsouth.net> writes:
>> [...]
>> One way is to divide the area under the bell curve into equal area
>> partitions. In this case 2^6 of them. The abscissal value for each of the
>> partitions becomes a transition point for the quantization. This
>> maximizes
>> the entropy (i.e., the information) since each quantization will be
>> equally
>> represented. And the entopy is maximized when each state has equal
>> probability.
>
> Isn't this a mapping from Gaussian to uniform? And we all know that
> uniform has the greatest entropy.

Basically except for the lack of a Jacobian. And going to a form which
maximizes our entropy is the goal.

>
> Is this related to the concept of "vector quantization"?

Probably - but I havn't done much with this, so I'll have to guess here. But
since the concept of maximizing entropy is a wonderful way of handling
quantization without history, so I would be surprised if it hasn't been used
for quantizing vocoder vectors. Remember in all of this process, we are
assuming no sample to sample correlation. And in speech this is not quite
true.

>
>> This in not unlike Huffman's idea where his coding scheme
>> attempts to make the length of each symbol times its frequency of
>> occurance
>> be the same for all symbols.
>
> I'm having trouble with this. Yes, I see that a Huffman code attempts to
> make
> (symbol length)*(symbol frequency) constant over all symbols. How does
> change
> anything about the underlying distribution, though?

The idea is to try to make each symbol contribute equally to the overall
process. Imagine looking at your data after a huge number of symbols was
received. The idea is to make the info provided by each type of symbol
contribute equally. And in data compression, the idea is to find the minimum
size for all of the data for a fixed information content.

I hope this helps.

Clay

> --
> Randy Yates
> Sony Ericsson Mobile Communications
> Research Triangle Park, NC, USA
> randy.yates@sonyericsson.com, 919-472-1124

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