Implications of Nyquist? ?????

On May 28, 12:24&#4294967295;pm, Richard Owlett <rowl...@atlascomm.net> wrote:
[snip]
>
> Just saying "Nyquist criterion" implies a *WRONG* 'universe of
> discourse' in subtle ways due to vagaries of English semantics (formal
> vs informal vs &#4294967295;jargon {technical or other}). Limiting it to signals (by
> implication) expressible by a time varying voltage between a pair of
> conductors *AND* examining how they may be decomposed and _RECONSTRUCTED_.

I don't follow how it is limited to voltage signals.  Are you
referring to Nyquist's original paper or something else?

> That "RECONSTRUCTED" is the key.

Yes, this is important.  And in fact, this is the key insight to
being able to reconstruct parametric signals that are sampled
below the Nyquist rate.

> My question arises out of an interest in a subset of speech recognition
> - phoneme recognition (could be thought of as a portion of finite
> vocabulary discrete speech). I won't pose my question in those terms as
> I'd likely misuse some technical terms - I know more than I grok. (Thank
> you Mr. Heinlein)
>
> I'll try to pose my question in terms of "text to speech" instead.
> The input will be 1 page of printed text (cf time limited).
> It will be straight declarative sentences (no ! or ?) (cf band limited).
> Following the example using "Lena" and "Mona Lisa" as image compression
> test cases, I'll specify printed copies of Lincoln's "Gettysburg
> Address" as the input.
>
> The test of "fidelity" would be an ideal court stenographer transcribing
> using IPA and reading back the text, which would be independent of input
> being 10 point Courier Regular or 15 point Garmond Bold Italic etc.
>
> Something is remaining the same. In my original post, when I used the
> term "information" I was referring to "information" gained by listening
> to the stenographer reading back the text.
>
> What key word(s) should I investigate?
>
> Thank you.

Let me try to express what I think you just said mathematically.
The source of message generates a sequence of letters, probably
following a certain distribution or language rules.

Then, this sequence of letters is mapped onto pieces of paper
using a certain font, spacing, etc.

An observer observes a degraded version of these papers somehow.
The observer knows the distribution of sequences or the language
rules.  Then how much degradation can be applied on the
observation such that an observer can still reconstruct the original
message with high fidelity.

Does this sound about right?

Julius

clay@claysturner.com wrote:
> On May 17, 3:38 pm, Richard Owlett <rowl...@atlascomm.net> wrote:
> 
>>_TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to
>>sample a waveform at >= a particular frequency.
>>
>>I've gut feeling that Nyquist implies more.
>>
>>I suspect it's more about information transfer rate.
>>
>>What question should I be asking.
>>
>>Signed
>>ADMITTED *STUPIDENT*
> 
> 
> Hello Richard,
> 
> The following paper is most excellent, and I believe will more than
> answer your questions.
> 
> http://www.imagescience.org/meijering/publications/download/pieee2002.pdf
> 
> Clay Turner
> 

Thank you, it provided needed perspective.
Nyquist et al. has nothing to do with with the question I was trying to 
formulate. (cf Just because because trains leaving NYC for Washington 
and California may use the same track for a while does not mean that 
have anything to do with each other.)

glen herrmannsfeldt wrote:

> clay@claysturner.com wrote:
> (snip)
>  
> 
>>The following paper is most excellent, and I believe will more than
>>answer your questions.
> 
>  
> 
>>http://www.imagescience.org/meijering/publications/download/pieee2002.pdf
> 
> 
> I would also recommend reading Nyquist's paper, though I don't
> know that it is available on the web.  It should be easy to
> find in a big university library, or maybe even a small one.
> 
> -- glen

Snicker. I'm in *RURAL* SW Missouri - livestock outnumber people. 
Suspect nearest library that would have it is 3 hours away.

clay@claysturner.com wrote:

> On May 29, 3:40 pm, c...@claysturner.com wrote:
> 
>>On May 29, 3:09 pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
>>
>>
>>>c...@claysturner.com wrote:
>>
>>>(snip)
>>
>>>>The following paper is most excellent, and I believe will more than
>>>>answer your questions.
>>>>http://www.imagescience.org/meijering/publications/download/pieee2002...
>>
>>>I would also recommend reading Nyquist's paper, though I don't
>>>know that it is available on the web.  It should be easy to
>>>find in a big university library, or maybe even a small one.
>>
>>>-- glen
>>
>>I agree, I just thought I'd point Richard to something on the web.
>>
>>Clay
> 
> 
> It may help to know the Nyquist's article was reprinted:
> 
> "Certain Topics in Telegraph Transmission Theory", Nyquist, Harry,
> Proc. IEEE, Vol 90, No 2, Feb 2002
> 

That version exists on the web in Greece and Argentina, right down to 
IEEE copyright notice. Now I have to read it.

> 
> FWIW,
> 
> Clay

julius wrote:

> On May 28, 12:24 pm, Richard Owlett <rowl...@atlascomm.net> wrote:
> [snip]
> 
>>Just saying "Nyquist criterion" implies a *WRONG* 'universe of
>>discourse' in subtle ways due to vagaries of English semantics (formal
>>vs informal vs  jargon {technical or other}). Limiting it to signals (by
>>implication) expressible by a time varying voltage between a pair of
>>conductors *AND* examining how they may be decomposed and _RECONSTRUCTED_.
> 
> 
> I don't follow how it is limited to voltage signals.  Are you
> referring to Nyquist's original paper or something else?

I was misapplying Nyquist. See my replies to Glen and Clay.

> 
> 
>>That "RECONSTRUCTED" is the key.
> 
> 
> Yes, this is important.  And in fact, this is the key insight to
> being able to reconstruct parametric signals that are sampled
> below the Nyquist rate.
> 
> 
>>My question arises out of an interest in a subset of speech recognition
>>- phoneme recognition (could be thought of as a portion of finite
>>vocabulary discrete speech). I won't pose my question in those terms as
>>I'd likely misuse some technical terms - I know more than I grok. (Thank
>>you Mr. Heinlein)
>>
>>I'll try to pose my question in terms of "text to speech" instead.
>>The input will be 1 page of printed text (cf time limited).
>>It will be straight declarative sentences (no ! or ?) (cf band limited).
>>Following the example using "Lena" and "Mona Lisa" as image compression
>>test cases, I'll specify printed copies of Lincoln's "Gettysburg
>>Address" as the input.
>>
>>The test of "fidelity" would be an ideal court stenographer transcribing
>>using IPA and reading back the text, which would be independent of input
>>being 10 point Courier Regular or 15 point Garmond Bold Italic etc.
>>
>>Something is remaining the same. In my original post, when I used the
>>term "information" I was referring to "information" gained by listening
>>to the stenographer reading back the text.
>>
>>What key word(s) should I investigate?
>>
>>Thank you.
> 
> 
> Let me try to express what I think you just said mathematically.
> The source of message generates a sequence of letters, probably
> following a certain distribution or language rules.
> 
> Then, this sequence of letters is mapped onto pieces of paper
> using a certain font, spacing, etc.
> 
> An observer observes a degraded version of these papers somehow.
> The observer knows the distribution of sequences or the language
> rules.  Then how much degradation can be applied on the
> observation such that an observer can still reconstruct the original
> message with high fidelity.
> 
> Does this sound about right?

Better than what I wrote. But I've thought of a better analogy, now that 
I realize that Nyquist could be a red herring. Some (most?) ancient 
Greek manuscripts were written in all one case without spaces between 
words or any punctuation marks. Can make parsing difficult, especially 
when the document is damaged (i.e. noisy). You have to look finely 
enough to identify the individual characters - to fine would create 
another set of problems. Then again you have to look wider to identify 
words and some words might be unlikely due to overall context.


> 
> Julius