> >Some say that this Russian Kotelnikov has precedence over both.
> >According to a discussion I had a couple of days ago, the French
> >mathematician Cauchy developed sampling theorey well before any of the
> >above three was born. It will probably turn out that Euler discovered
> >and stated the sampling theorem before him, and Archimedes before
> >Euler. It might well be that Newton and Leibniz also argued about it in
> >secret anagram communications. Oh, and don't forget Tesla - somewhere
> >in his papers, there _must_ be something as trivial as the sampling
> >theorem.Hi Andor,
> I thought Al Gore developed the Nyquist Sampling
> Theorem.
:-D
Reply by Rick Lyons●December 21, 20062006-12-21
On 20 Dec 2006 23:18:51 -0800, "Andor" <andor.bariska@gmail.com>
wrote:
>
>
>Sanctus wrote:
>> I doubt Nyquist said much at all - it was Shannon wasn't it?
>
>Some say that this Russian Kotelnikov has precedence over both.
>According to a discussion I had a couple of days ago, the French
>mathematician Cauchy developed sampling theorey well before any of the
>above three was born. It will probably turn out that Euler discovered
>and stated the sampling theorem before him, and Archimedes before
>Euler. It might well be that Newton and Leibniz also argued about it in
>secret anagram communications. Oh, and don't forget Tesla - somewhere
>in his papers, there _must_ be something as trivial as the sampling
>theorem.
Hi Andor,
I thought Al Gore developed the Nyquist Sampling
Theorem.
[-Rick-]
Reply by Andor●December 21, 20062006-12-21
Sanctus wrote:
> I doubt Nyquist said much at all - it was Shannon wasn't it?
Some say that this Russian Kotelnikov has precedence over both.
According to a discussion I had a couple of days ago, the French
mathematician Cauchy developed sampling theorey well before any of the
above three was born. It will probably turn out that Euler discovered
and stated the sampling theorem before him, and Archimedes before
Euler. It might well be that Newton and Leibniz also argued about it in
secret anagram communications. Oh, and don't forget Tesla - somewhere
in his papers, there _must_ be something as trivial as the sampling
theorem.
Reply by Jerry Avins●December 20, 20062006-12-20
steve wrote:
> Ron N. wrote:
>> jjmai wrote:
>>> Let's say you have a perfect sine wave at frequency w.
>>> According to Nyquist, in order to be able to recover the sine wave, you
>>> need to have a sampling rate of at least 2w.
>>> So if you decide to sample at 2w, you end up with 2 samples for each cycle
>>> of this sine wave.
>> However the time it takes to recover the amplitude is proportional
>> to the reciprocal of how close your sampling rate is to 2w.
>
> can you expand upon that concept? derivation, assumptions, examples
> etc. thanks
I don't have time now, but it's probably enough that the time to resolve
(fs/2) - f is exactly the same as the time to resolve f to the same
degree of accuracy. when f is very small, the time is long either way.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by steve●December 20, 20062006-12-20
Ron N. wrote:
> jjmai wrote:
> > Let's say you have a perfect sine wave at frequency w.
> > According to Nyquist, in order to be able to recover the sine wave, you
> > need to have a sampling rate of at least 2w.
> > So if you decide to sample at 2w, you end up with 2 samples for each cycle
> > of this sine wave.
>
> However the time it takes to recover the amplitude is proportional
> to the reciprocal of how close your sampling rate is to 2w.
can you expand upon that concept? derivation, assumptions, examples
etc. thanks
Reply by Jerry Avins●December 20, 20062006-12-20
Mark wrote:
...
> well actually a pure sine wave has zero bandwidth so if you know the
> frequency, you don't need to sample it at all????
What if you don't? And what about amplitude and phase if you do?
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by Ray Andraka●December 20, 20062006-12-20
Vladimir Vassilevsky wrote:
>
>
> jjmai wrote:
>
>> Let's say you have a perfect sine wave at frequency w.
>> According to Nyquist, in order to be able to recover the sine wave, you
>> need to have a sampling rate of at least 2w.
>
>
> This is wrong.
>
> If you know that the signal is a perfect sine wave, all you need is 3
> samples to find the amplitude, the phase and the frequency.
>
> VLV
Provided the sample interval is not an integer multiple of the period of
the signal.
Reply by Tim Wescott●December 20, 20062006-12-20
Sanctus wrote:
> "Tim Wescott" <tim@seemywebsite.com> wrote in message
> news:64ednf87dpLYVxXYnZ2dnUVZ_tadnZ2d@web-ster.com...
>
>>jjmai wrote:
>>
>>
>>>Let's say you have a perfect sine wave at frequency w.
>>>According to Nyquist, in order to be able to recover the sine wave, you
>>>need to have a sampling rate of at least 2w.
>>>So if you decide to sample at 2w, you end up with 2 samples for each
>
> cycle
>
>>>of this sine wave.
>>>
>>>If you sample at the peaks and troughs (90 and 270 degrees) of the sine
>>>wave in time (or spatial) domain, you indeed preserve the amplitude.
>>>But what happens when the sampling happens at 0 and 180 degrees? You
>
> end
>
>>>up with only zeros.
>>>
>>>Am I missing something about sampling theorem here? Is a shifted
>
> sampling
>
>>>not the same as the origianl unshifted sampling?
>>>
>>>
>>
>>This question, and more, are answered in my article "Sampling: What
>>Nyquist Didn't Say, and What to Do About It", to be found at
>>http://www.wescottdesign.com/articles/Sampling/sampling.html.
>>
>>I hope it helps.
>>
>>--
>>
>>Tim Wescott
>>Wescott Design Services
>>http://www.wescottdesign.com
>>
>>Posting from Google? See http://cfaj.freeshell.org/google/
>>
>>"Applied Control Theory for Embedded Systems" came out in April.
>>See details at http://www.wescottdesign.com/actfes/actfes.html
>
>
> Actually I doubt Nyquist said much at all - it was Shannon wasn't it?
>
yea yea yea. Officially it's the Nyquist-Shannon theorem, or the
Shannon Sampling Theorem.
The title (the whole article, in fact) was a response to a spate of
newsgroup postings that started with "Nyquist says" and ended with some
naive conclusion that comes from taking an absolute limit as a design guide.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Posting from Google? See http://cfaj.freeshell.org/google/
"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Sanctus●December 20, 20062006-12-20
"Tim Wescott" <tim@seemywebsite.com> wrote in message
news:64ednf87dpLYVxXYnZ2dnUVZ_tadnZ2d@web-ster.com...
> jjmai wrote:
>
> > Let's say you have a perfect sine wave at frequency w.
> > According to Nyquist, in order to be able to recover the sine wave, you
> > need to have a sampling rate of at least 2w.
> > So if you decide to sample at 2w, you end up with 2 samples for each
cycle
> > of this sine wave.
> >
> > If you sample at the peaks and troughs (90 and 270 degrees) of the sine
> > wave in time (or spatial) domain, you indeed preserve the amplitude.
> > But what happens when the sampling happens at 0 and 180 degrees? You
end
> > up with only zeros.
> >
> > Am I missing something about sampling theorem here? Is a shifted
Actually I doubt Nyquist said much at all - it was Shannon wasn't it?
S.
--
Posted via a free Usenet account from http://www.teranews.com
Reply by Tim Wescott●December 20, 20062006-12-20
jjmai wrote:
> Let's say you have a perfect sine wave at frequency w.
> According to Nyquist, in order to be able to recover the sine wave, you
> need to have a sampling rate of at least 2w.
> So if you decide to sample at 2w, you end up with 2 samples for each cycle
> of this sine wave.
>
> If you sample at the peaks and troughs (90 and 270 degrees) of the sine
> wave in time (or spatial) domain, you indeed preserve the amplitude.
> But what happens when the sampling happens at 0 and 180 degrees? You end
> up with only zeros.
>
> Am I missing something about sampling theorem here? Is a shifted sampling
> not the same as the origianl unshifted sampling?
>
>