Re: how to find the best ADC step size?

From: glen herrmannsfeldt (gah_at_ugcs.caltech.edu)
Date: 12/22/04 

Date: Wed, 22 Dec 2004 10:33:42 -0800

Someone wrote:
>>>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?

> "Clay S. Turner" <Physics@Bellsouth.net> writes:
>>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.

Randy Yates wrote:
> But this Huffman coding won't do that. Choosing a representation for a
> symbol doesn't change the probability of the symbol occurring. It
> does, however, minize the average symbol rate - I certainly see
> that. Perhaps I'm being blind?

The gaussian has infinite tails, so it isn't possible to cover
the range with a linear scale ADC. One could then ask for what
part of the distribution, when covered with the steps of a six
bit ADC, are the symbol probabilities most equal.

Without doing the math it isn't so obvious either way.
For the case of a very large (lim --> infinity) most of
the symbols will have almost no probability. In the
limit of very small step size, and assuming that the lower
and upper step get the tails, again most steps have almost
no probability.

So, it would seem that somewhere in between the probability
would be more equal. One should then define the appropriate
function of step size and find the minimum point.

-- glen

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