Vladimir A. Kotelnikow died February 11, 2005... 8-(
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Reply by Airy R. Bean●November 17, 20042004-11-17
You're not describing a fictitious sampler which was the question put.
"Number 6" <No6@distant.island.nz> wrote in message
news:1100677357.781045@ftpsrv1...
> "Airy R. Bean" <me@privacy.net> wrote in message
> news:2vr8ufF2ook8qU2@uni-berlin.de...
> > Vague approximations are the stuff of technicians and not of engineers.
> > How do I connect a spectrum analyser to a fictitious sampler? Hardly
> > a respectable activity for a practising engineer!
> You get an analogue multiplier and use a pulse generator. Multiply the
> required signal by the impulse train and take the spectrum of the output-
> easy. I saw it done over 20 years ago. If you are worried about the width
of
> the pulses you need not be concerned as you can very the width and see
that
> it satisfies the modified sampling theory where the pulses have finite
> width.Of course if you know better then publish it or be dammed!
Reply by Airy R. Bean●November 17, 20042004-11-17
See lesson 3.
"Number 6" <No6@distant.island.nz> wrote in message
news:1100677435.865716@ftpsrv1...
> "Airy R. Bean" <me@privacy.net> wrote in message
> news:2vttalF2p3f09U1@uni-berlin.de...
> > And it is important to disambiguate between the theoretical
> > analysis undertaken in order to determine the minimum
> > frequency of sampling, from what is actually happening in
> > sampling circuits to get our samples. To treat the latter
> > as an extension of the former is to make a category error.
> Fine but we are still waiting your mathematical explanation!
Reply by Number 6●November 17, 20042004-11-17
"Airy R. Bean" <me@privacy.net> wrote in message
news:2vttalF2p3f09U1@uni-berlin.de...
> And it is important to disambiguate between the theoretical
> analysis undertaken in order to determine the minimum
> frequency of sampling, from what is actually happening in
> sampling circuits to get our samples. To treat the latter
> as an extension of the former is to make a category error.
>
Fine but we are still waiting your mathematical explanation!
Tom
Reply by Number 6●November 17, 20042004-11-17
"Airy R. Bean" <me@privacy.net> wrote in message
news:2vr8ufF2ook8qU2@uni-berlin.de...
> Vague approximations are the stuff of technicians and not of engineers.
>
>
> How do I connect a spectrum analyser to a fictitious sampler? Hardly
> a respectable activity for a practising engineer!
>
>
You get an analogue multiplier and use a pulse generator. Multiply the
required signal by the impulse train and take the spectrum of the output-
easy. I saw it done over 20 years ago. If you are worried about the width of
the pulses you need not be concerned as you can very the width and see that
it satisfies the modified sampling theory where the pulses have finite
width.Of course if you know better then publish it or be dammed!
Tom
Reply by Airy R. Bean●November 16, 20042004-11-16
And it is important to disambiguate between the theoretical
analysis undertaken in order to determine the minimum
frequency of sampling, from what is actually happening in
sampling circuits to get our samples. To treat the latter
as an extension of the former is to make a category error.
"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message
news:cnb8e3$udg$1@gnus01.u.washington.edu...
> As mentioned somewhere else in this newsgroup, Nyquist was actually
> working on how fast telegraph signals could be sent through a band
> limited system and be reliably separated at the other end.
Reply by Jerry Avins●November 15, 20042004-11-15
Clay Turner wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message
> news:2vsqvtF2ovfplU1@uni-berlin.de...
>
>>glen herrmannsfeldt wrote:
>>
>>
>>Consider also microscope objectives. With them, resolution depends on on
>>the fraction of a sphere (centered on the object) that the lens
>>subtends, and not directly on the lens' diameter. Hmm ...
>
>
> Jerry,
>
> Kirchoff's Obliquity Factor is the big problem with low F number lenses.
> This is why the effective diameter (found by using Rayleigh's formula in
> reverse) is smaller than the true diameter.
As far as I know, it doesn't apply either to immersion objectives or to
those whose front element is a hyper-hemispheric meniscus.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Clay Turner●November 15, 20042004-11-15
"Jerry Avins" <jya@ieee.org> wrote in message
news:2vsqvtF2ovfplU1@uni-berlin.de...
> glen herrmannsfeldt wrote:
>
> >
>
> Consider also microscope objectives. With them, resolution depends on on
> the fraction of a sphere (centered on the object) that the lens
> subtends, and not directly on the lens' diameter. Hmm ...
Jerry,
Kirchoff's Obliquity Factor is the big problem with low F number lenses.
This is why the effective diameter (found by using Rayleigh's formula in
reverse) is smaller than the true diameter.
Clay
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
Reply by Jerry Avins●November 15, 20042004-11-15
glen herrmannsfeldt wrote:
>
>
> Clay Turner wrote:
> (snip)
>
>> Yes, Whittacker, Kotelnikov,, and Nyquist each worked out some details
>> about
>> the components of what we now know as the sampling theorem. And others
>> did
>> too. Shannon formalized the results into a single theorem. He also stated
>> that there was nothing new in this theorem and that what it
>> encompassed was
>> already well known. Shannon used this theorem simply as a launching point
>> for his noisy sampling theorem and information theory.
>
>
> As mentioned somewhere else in this newsgroup, Nyquist was actually
> working on how fast telegraph signals could be sent through a band
> limited system and be reliably separated at the other end. Through some
> symmetry operations, this can be converted to what is now Nyquist
> sampling. Consider also the optics problem of image resolution
> and lens diameter, where larger lenses are needed to resolve the
> separation of images with fine detail.
Consider also microscope objectives. With them, resolution depends on on
the fraction of a sphere (centered on the object) that the lens
subtends, and not directly on the lens' diameter. Hmm ...
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by glen herrmannsfeldt●November 15, 20042004-11-15
Clay Turner wrote:
(snip)
> Yes, Whittacker, Kotelnikov,, and Nyquist each worked out some details about
> the components of what we now know as the sampling theorem. And others did
> too. Shannon formalized the results into a single theorem. He also stated
> that there was nothing new in this theorem and that what it encompassed was
> already well known. Shannon used this theorem simply as a launching point
> for his noisy sampling theorem and information theory.
As mentioned somewhere else in this newsgroup, Nyquist was actually
working on how fast telegraph signals could be sent through a band
limited system and be reliably separated at the other end. Through some
symmetry operations, this can be converted to what is now Nyquist
sampling. Consider also the optics problem of image resolution
and lens diameter, where larger lenses are needed to resolve the
separation of images with fine detail.
-- glen