This is due to Whittaker E. T. Whittaker, On the functions which are represented by the expansions of the interpolation theory, Proc. Roy. Soc. Edinburgh 35 (1915), 181-194 http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Whittaker.html and to Kotelnikov V. A. Kotelnikov, On the carrying capacity of the ether and wire in telecommunications, Material for the First All-Union Conference on Questions of Communication, Izd. Red. Upr. Svyazi RKKA, Moskow, 1933 (Russian). http://ieee.orbita.ru/Sampl_Theorem_Conf.htm I think he may well eb still alive! http://www.cplire.ru/html/kotelnikov.html also Shannon C. E. Shannon, Communication in the presence of noise, Proc. IRE 37 (1949), 10-21. and the Swede Harry Nyquist H. Nyquist, Certain topics in telegraph transmission theory, Trans. AIEE, vol. 47, pp. 617-644, Apr. 1928 Therefore we should say we have the Whittaker-Nyquist sampling theory - why Shannon - he came in fourth? Tom
The Sampling theorem
Started by ●November 12, 2004
Reply by ●November 13, 20042004-11-13
"Number 6" <No6@distant.island.nz> wrote in message news:<1100308020.788102@ftpsrv1>... [...]> Therefore we should say we have the > > Whittaker-Nyquist sampling theory - why Shannon - he came in fourth?Well, politics does have a part in it. The theorem on refraction of rays I know as "Snell's Law", is apparently referred to by the French as "Descare's Law". I *think* I have seen somewehere that the Russians attribute the same theorem to some Russian scientist, although I am not sure about that. Being Norwegian, I find it very interesting that the 1911 race to reach the South Pole (which was won by the Norwegian Roald Amundsen) in international (i.e. British) fora unanimuosly is approached along the lines of the "heroism" of Scott monumentous screw-up where the whole expetdition team was lost, due to what seems to be very poor preparations. Such reviews mention the fact that Scott's crew found Amundsen's tent and flag at the pole point merely in passing. More recently, most discussions of the world speed record for "cars", set by the Thrust SSC in, was it 1998?, fails to mention the Budweisser Rocket that broke the sound barrier in 1978-79. The Budweisser Rocket failed to meet certain requirements set by the FIA to both the technical construction of the vehicle and the exercusion of the record attempt, and could thus not claim the official records. Still, it was the first "car" to break the sound barrier, an honor now attributed to the Thrust SSC which was the first to do it by FIA rules. It's basically a matter of convenience, or rather, coincidence, who recieves the historical credit for what feat. Rune
Reply by ●November 13, 20042004-11-13
"Number 6" <No6@distant.island.nz> wrote in message news:1100308020.788102@ftpsrv1...> This is due to Whittaker >> Therefore we should say we have the > > Whittaker-Nyquist sampling theory - why Shannon - he came in fourth? > > Tom > >Hello Tom, 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. Many scholars now refer to the sampling theorem as the WKS sampling theorem. See the below links for more detail. Unser explains on the 1st page why Shannon gets credit. "A Chronology of Interpolation" at http://imagescience.bigr.nl/meijering/publications/download/pieee2002.pdf "Sampling--50 years after Shannon" http://bigwww.epfl.ch/publications/unser0001.pdf Clay
Reply by ●November 14, 20042004-11-14
In order to prove my viewpoints relating to a sound mathematical basis for the engineer's sampling, I think that it will be necessary to identify the point in history where the faulty meme about sampling being a multiplication of a signal by a comb of dirac delta functions first arose, and then to show that it was either faulty, or not based upon some previous thesis or not based upon some axiom. In pursuit of this objective, I am having difficulty in finding on the web, an original transcript of Nyquist's 1924 paper, "Certain Factors Affecting Telegraph Speed", or a retyping of it without others' commentaries. Can anyone provide a URL? "Clay Turner" <physics@bellsouth.net> wrote in message news:zTpld.10970$WC6.10378@bignews3.bellsouth.net...> Yes, Whittacker, Kotelnikov,, and Nyquist each worked out some detailsabout> 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 encompassedwas> already well known. Shannon used this theorem simply as a launching point > for his noisy sampling theorem and information theory.
Reply by ●November 14, 20042004-11-14
"Airy R. Bean" <me@privacy.net> wrote in message news:2voqchF2m350bU2@uni-berlin.de...> In order to prove my viewpoints relating to a sound mathematical basis > for the engineer's sampling, I think that it will be necessary to > identify the point in history where the faulty meme about sampling > being a multiplication of a signal by a comb of dirac delta functionsfirst> arose, and then to show that it was either faulty, or not based upon > some previous thesis or not based upon some axiom. > > In pursuit of this objective, I am having difficulty in finding on theweb,> an original transcript of Nyquist's 1924 paper, "Certain Factors Affecting > Telegraph Speed", or a retyping of it without others' commentaries. > > Can anyone provide a URL? > >Not all papers have a URL! You may need to go inter library loan and pay for it. However, I would have thought such an important paper was somewhere on the web. You're wasting your time in any case - the experimental results match the theory and this is good for most of us.You can make your own fictitious sampler by creating an impulse (approx) train and use an analogue multiplier. Look (with a spectrum analyser) at the spectrum of the sampled signal and you will see that it fits the theory nicely. Of course the pulses will not be true impulses and we can account for that too.It is pretty basic stuff and not worthy of a re-visit. Tom
Reply by ●November 15, 20042004-11-15
Vague approximations are the stuff of technicians and not of engineers. To which experimental results do you appeal? Where published? To which theory are you referring? Nyquist's sampling, perhaps? If so, Nyquist's sampling theory relates to the analysis of the minimum sampling frequency required. It does not refer to the analysis of what is going on in real engineering circuits. Real Engineers wish to use figures that apply to the circuits on the bench in front of them. How do I connect a spectrum analyser to a fictitious sampler? Hardly a respectable activity for a practising engineer! "Number 6" <No6@distant.island.nz> wrote in message news:1100479163.94669@ftpsrv1...> "Airy R. Bean" <me@privacy.net> wrote in message > news:2voqchF2m350bU2@uni-berlin.de... > > In order to prove my viewpoints relating to a sound mathematical basis > > for the engineer's sampling, I think that it will be necessary to > > identify the point in history where the faulty meme about sampling > > being a multiplication of a signal by a comb of dirac delta functions > first > > arose, and then to show that it was either faulty, or not based upon > > some previous thesis or not based upon some axiom. > > In pursuit of this objective, I am having difficulty in finding on the > web, > > an original transcript of Nyquist's 1924 paper, "Certain FactorsAffecting> > Telegraph Speed", or a retyping of it without others' commentaries. > > Can anyone provide a URL? > Not all papers have a URL! You may need to go inter library loan and payfor> it. > However, I would have thought such an important paper was somewhere on the > web. > You're wasting your time in any case - the experimental results match the > theory and this is good for most of us.You can make your own fictitious > sampler by creating an impulse (approx) train and use an analogue > multiplier. Look (with a spectrum analyser) at the spectrum of the sampled > signal and you will see that it fits the theory nicely. > Of course the pulses will not be true impulses and we can account for that > too.It is pretty basic stuff and not worthy of a re-visit.
Reply by ●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
Reply by ●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 ●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 ●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. �����������������������������������������������������������������������
