Shenon's theorem proving
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From: st256 on 6 Apr 2010 02:07 > >"Shenon"? > >might you mean "Shannon"? if so, which one? the Sampling theorem >(often associated with other names like Nyquist or Whittaker or >Kotelnikov)? the information content of a message? the channel >information capacity theorem (Shannon-Hartley)? > >dunno about the rooskie version of Wikipedia, but the english version >has proofs, i think. > >r b-j > Thank you very much! Of course, I meaned "Shannon", sorry! There is the authentic Shannon's proof in Wikipedia indeed. I look for a correct proof of sampling theorem because authentic proofs sometimes are not correct one enough.
From: Les Cargill on 6 Apr 2010 20:03 st256 wrote: >> >> "Shenon"? >> >> might you mean "Shannon"? if so, which one? the Sampling theorem >> (often associated with other names like Nyquist or Whittaker or >> Kotelnikov)? the information content of a message? the channel >> information capacity theorem (Shannon-Hartley)? >> >> dunno about the rooskie version of Wikipedia, but the english version >> has proofs, i think. >> >> r b-j >> > > Thank you very much! > > Of course, I meaned "Shannon", sorry! > There is the authentic Shannon's proof in Wikipedia indeed. I look for a > correct proof of sampling theorem because authentic proofs sometimes are > not correct one enough. The Wikipedia one is fine. -- Les Cargill
From: robert bristow-johnson on 6 Apr 2010 23:44 On Apr 6, 8:03 pm, Les Cargill <lcargil...(a)comcast.net> wrote: > st256 wrote: > > >> "Shenon"? > > >> might you mean "Shannon"? if so, which one? the Sampling theorem > >> (often associated with other names like Nyquist or Whittaker or > >> Kotelnikov)? the information content of a message? the channel > >> information capacity theorem (Shannon-Hartley)? > > >> dunno about the rooskie version of Wikipedia, but the english version > >> has proofs, i think. > > > There is the authentic Shannon's proof in Wikipedia indeed. I look for a > > correct proof of sampling theorem because authentic proofs sometimes are > > not correct one enough. > > The Wikipedia one is fine. > well, it all depends on how anal one wants to get regarding the dirac impulse and dirac comb. if you want to make your math prof happy, perhaps http://en.wikipedia.org/wiki/Poisson_summation_formula will be more rigorous. but i am comfortable with the "engineering" definition and usage of the dirac delta function, so the proof in Nyquist-Shannon sampling theorem is good enough for me. r b-j
From: Clay on 7 Apr 2010 11:14
On Apr 6, 11:44 pm, robert bristow-johnson <r...(a)audioimagination.com> wrote: > On Apr 6, 8:03 pm, Les Cargill <lcargil...(a)comcast.net> wrote: > > > > > > > st256 wrote: > > > >> "Shenon"? > > > >> might you mean "Shannon"? if so, which one? the Sampling theorem > > >> (often associated with other names like Nyquist or Whittaker or > > >> Kotelnikov)? the information content of a message? the channel > > >> information capacity theorem (Shannon-Hartley)? > > > >> dunno about the rooskie version of Wikipedia, but the english version > > >> has proofs, i think. > > > > There is the authentic Shannon's proof in Wikipedia indeed. I look for a > > > correct proof of sampling theorem because authentic proofs sometimes are > > > not correct one enough. > > > The Wikipedia one is fine. > > well, it all depends on how anal one wants to get regarding the dirac > impulse and dirac comb. > > if you want to make your math prof happy, perhaps > > http://en.wikipedia.org/wiki/Poisson_summation_formula > That's a nice writeup on the Poisson formula. I learned of the formula from the "Hand of Integration" (Zwillinger) which is full of many tricks for handling seemingly impossible integrals. Thx, Clay |