Implications of Nyquist? ?????

On May 17, 3:38&#4294967295;pm, Richard Owlett <rowl...@atlascomm.net> wrote:
> _TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to
> sample a waveform at >= a particular frequency.

actually strictly >.  the particular frequency is twice the highest
frequency ever expected in the content of the continuous-time signal.

> I've gut feeling that Nyquist implies more.

you mean the theorem with his name in it (that everyone says is better
attributed to Whittaker, Shannon, Kotelnikov, and/or Raabe)

> I suspect it's more about information transfer rate.

information transfer rate needs to know information about S/N which
the basic Sampling Theorem doesn't concern itself with.  the capacity
rate of transfer of information through a channel is

              B
    C = integral{ log2( (S+N)/N ) df }
              0

where S = S(f) = signal power spectrum
      N = N(f) = noise power spectrum
      B = upper Bandwidth (no S(f) for f>B)

      C = channel capacity in bits per unit time (if base-2 log is
used)

> What question should I be asking.

i dunno.  i dunno what it is you want.

r b-j

On Sun, 17 May 2009 22:55:48 -0400, Jerry Avins wrote:

> Tim Wescott wrote:
> 
>    ...
> 
>> If I am not mistaken an absolutely band limited signal _is_ of limited
>> duration, which is one of the salient features that makes it impossible
>> to be real world.
> 
> Erm .. unlimited duration?

Yes, quite.  _Un_ limited duration, or infinite duration, or just about 
any duration that goes on forever and ever and ever.

I was out in the hot sun all day today, burning about three yards of 
brush.  I think I fried some brain cells.  (This doesn't explain the 
times I mistype things when I'm supposedly doing _well_).

-- 
www.wescottdesign.com

On Sun, 17 May 2009 20:01:05 -0700, dvsarwate@yahoo.com wrote:

> On May 17, 9:22&nbsp;pm, Tim Wescott <t...@seemywebsite.com> wrote:
>> On Sun, 17 May 2009 23:02:45 +0000, glen herrmannsfeldt wrote:
>> > Tim Wescott <t...@seemywebsite.com> wrote:
>>
>>
>> If I am not mistaken an absolutely band limited signal _is_ of limited
>> duration, which is one of the salient features that makes it impossible
>> to be real world.
> 
> That is, the signal is limited in **both** frequency and time?  I don't
> believe that this is correct.  A signal that is absolutely limited in
> one domain extends to plus/minus infinity in the other domain.  A
> strictly band-limited signal is of infinite duration, and a strictly
> time-limited
> signal has Fourier transform that is nonzero for arbitrarily large
> values
> of frequency.

You are correct; I mistyped.  I had the image of a signal of infinite 
extent in time when I typed "limited duration".  The "un" fell off and is 
probably hiding under my desk ready to bite my ankle when I'm not 
watching.

-- 
www.wescottdesign.com

robert bristow-johnson <rbj@audioimagination.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.
 
> actually strictly >.  the particular frequency is twice the highest
> frequency ever expected in the content of the continuous-time signal.

Well, since we already decided that it only applies to infinite
durations signals, and we very rarely have one of those, it will
be rare that we have a chance to tell the difference 
between > and >= in actual measurement.  In addition, if you
have a tolerance on the frequency source that is likely to
cover the difference.
 
>> I've gut feeling that Nyquist implies more.

I used to have a copy of the original Nyquist paper.  You can
probably find it in a nearby university library.
 
> you mean the theorem with his name in it (that everyone says is better
> attributed to Whittaker, Shannon, Kotelnikov, and/or Raabe)
 
>> I suspect it's more about information transfer rate.

Yes.
 
> information transfer rate needs to know information about S/N which
> the basic Sampling Theorem doesn't concern itself with.  the capacity
> rate of transfer of information through a channel is
 
>> What question should I be asking.

Read the paper.  It is interesting to read, especially seeing
what has changed over the years and what has not changed.

-- glen

Richard Owlett dug myself into semantic traps saying:
> _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.
> 

Julius referred me to an article on "rate of innovation". That seemed a 
good candidate for a search term ---- until I read its first paragraph.

I then Googled for ( Whittaker Shannon Kotelnikov Raabe et al.)
The Wikipedia article "Nyquist�Shannon sampling theorem" spotlighted 
some semantic problems.

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_.

That "RECONSTRUCTED" is the key.

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.

Richard Owlett wrote:
> Richard Owlett dug myself into semantic traps saying:

ARGGH - the problems of line wrapping when adding emphasis to quoted 
text. I'll edit with explicit CR-LF and hope it comes thru better.

> 
>> _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.
>>
> 
> Julius referred me to an article on "rate of innovation". That seemed a 
> good candidate for a search term ---- until I read its first paragraph.
> 
> I then Googled for ( Whittaker Shannon Kotelnikov Raabe et al.)
> The Wikipedia article "Nyquist�Shannon sampling theorem" spotlighted 
> some semantic problems.
> 
> 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_.
> 
> That "RECONSTRUCTED" is the key.
> 
> 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.
> 
> 
> 
> 
> 
> 
> 

On May 17, 3:38&#4294967295;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

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

On May 29, 3:09&#4294967295;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. &#4294967295;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

On May 29, 3:40�pm, c...@claysturner.com wrote:
> On May 29, 3:09&#4294967295;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. &#4294967295;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


FWIW,

Clay