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Basic Sampling Theory Question

Started by old_ee August 17, 2015
On Tue, 18 Aug 2015 22:43:17 +0000 (UTC), spope33@speedymail.org
(Steve Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >>On Tue, 18 Aug 2015 19:01:05 +0000 (UTC), glen herrmannsfeldt > >>>And Nyquist had what seems to be a completely different problem. > >>>He wanted to know how fast he could send telegraph pulses through >>>a cable, and still see them at the other end. Turns out to be >>>the dual problem for sampling theory. > >>That's why the pulse-shaping filters in a communication system are >>called Nyquist filters. > >Okay, so that's what a Nyquist filter is. > >I had always figured it meant a filter that bandlimits a >signal such that it falls within the Nyquist limiq. > >Steve
The Nyquist filter in the receiver matches the pulse shape such that there is zero inter-symbol-interference (and presumably max SNR) at the desired sampling point (typically the middle of the pulse). A common desired pulse shape for zero-ISI is Raised Cosine, and usually the pulse shaping is split between the modulator (to limit the transmit BW) and the receiver, so the factored filter shapes are Square-Root-Raised-Cosine. The Tx and Rx filters then match each other to maintain the zero-ISI property (which is a sort-of overloaded case of "matched filter" terminology). Nyquist figured this out in the context of automated telegraph machines, so that the dispersion in the transmission lines didn't cause ISI at distant receivers. This allowed the transmission rate to be increased and transmit power to be reduced. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

>On Tue, 18 Aug 2015 22:43:17 +0000 (UTC), spope33@speedymail.org
>> Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>>>That's why the pulse-shaping filters in a communication system are >>>called Nyquist filters.
>>Okay, so that's what a Nyquist filter is.
>>I had always figured it meant a filter that bandlimits a >>signal such that it falls within the Nyquist limiq.
>The Nyquist filter in the receiver matches the pulse shape such that >there is zero inter-symbol-interference (and presumably max SNR) at >the desired sampling point (typically the middle of the pulse). A >common desired pulse shape for zero-ISI is Raised Cosine, and usually >the pulse shaping is split between the modulator (to limit the >transmit BW) and the receiver, so the factored filter shapes are >Square-Root-Raised-Cosine. The Tx and Rx filters then match each >other to maintain the zero-ISI property (which is a sort-of overloaded >case of "matched filter" terminology).
>Nyquist figured this out in the context of automated telegraph >machines, so that the dispersion in the transmission lines didn't >cause ISI at distant receivers. This allowed the transmission rate >to be increased and transmit power to be reduced.
Okay. But I am curious, which authors call these "Nyquist filters"? If for example, I look in Van Trees 1968, there's discussion of pulse-shaping and matched filters, but (based on the author index) the only reference to Nyquist is for the sampling theorem. Steve
On 8/18/15 7:52 PM, Eric Jacobsen wrote:
> On Tue, 18 Aug 2015 22:43:17 +0000 (UTC), spope33@speedymail.org > (Steve Pope) wrote: > >> Eric Jacobsen<eric.jacobsen@ieee.org> wrote: >> >>> On Tue, 18 Aug 2015 19:01:05 +0000 (UTC), glen herrmannsfeldt >> >>>> And Nyquist had what seems to be a completely different problem. >> >>>> He wanted to know how fast he could send telegraph pulses through >>>> a cable, and still see them at the other end. Turns out to be >>>> the dual problem for sampling theory. >> >>> That's why the pulse-shaping filters in a communication system are >>> called Nyquist filters. >> >> Okay, so that's what a Nyquist filter is. >> >> I had always figured it meant a filter that bandlimits a >> signal such that it falls within the Nyquist limiq. >> > > The Nyquist filter in the receiver matches the pulse shape such that > there is zero inter-symbol-interference (and presumably max SNR) at > the desired sampling point (typically the middle of the pulse). A > common desired pulse shape for zero-ISI is Raised Cosine, and usually > the pulse shaping is split between the modulator (to limit the > transmit BW) and the receiver, so the factored filter shapes are > Square-Root-Raised-Cosine. The Tx and Rx filters then match each > other to maintain the zero-ISI property (which is a sort-of overloaded > case of "matched filter" terminology). > > Nyquist figured this out in the context of automated telegraph > machines, so that the dispersion in the transmission lines didn't > cause ISI at distant receivers. This allowed the transmission rate > to be increased and transmit power to be reduced.
just FYI, although decades separate, Harry Nyquist and i are alumns of the same school and it ain't the University of *South* Dakota. :-) -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
On 8/17/2015 8:47 AM, Richard Dobson wrote:
> On 17/08/2015 11:29, old_ee wrote: >> Hi, >> >> If I have a sine wave with period T. The sampling theory says I can >> recover it by sampling at T/2. That is two points, barely enough to >> draw a >> straight line. >> >> What am I missing here? >> > > Reconstruction does not use straight lines.
In particular it should be considered that with the sample period equal to a single wavelength (or very close) the only waveforms that can be described are frequency 0 and 1 (normalized). I think that is what the OP is "missing". -- Rick
On 18.08.2015 21:29, gyansorova@gmail.com wrote:
(snip)

> Just a small correction, sampling theory was not due to Nyquist and Shannon but Whittaker and a Russian gentleman. Shannon just put it in an engineering framework. >
That gentleman's name is Kotelnikov. http://en.wikipedia.org/wiki/Vladimir_Kotelnikov Evgeny.
On Wed, 19 Aug 2015 22:52:52 +0300, Evgeny Filatov
<e.v.filatov@ieee.org> wrote:

>On 18.08.2015 21:29, gyansorova@gmail.com wrote: >(snip) > >> Just a small correction, sampling theory was not due to Nyquist and Shannon but Whittaker and a Russian gentleman. Shannon just put it in an engineering framework. >> > >That gentleman's name is Kotelnikov. > >http://en.wikipedia.org/wiki/Vladimir_Kotelnikov > >Evgeny. >
It's sad that the cold war kept a lot of science and engineering developments of the two sides separated for so long. I hope that doesn't ever happen again. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
On 19.08.2015 23:51, Eric Jacobsen wrote:

(snip)

> It's sad that the cold war kept a lot of science and engineering > developments of the two sides separated for so long. I hope that > doesn't ever happen again. > > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com >
While I agree with that perspective, at the end of the day getting things right is more important than memorizing the right names, as captured in that webcomic: http://www.phdcomics.com/comics/archive.php?comicid=976 Currently there is simply a greater variety of technical books in English than in any other language. Much to the dismay of my wife :) I keep spending a fraction of my wage buying DSP/comm books which are predominantly in English. Evgeny.
On 19.08.2015 23:51, Eric Jacobsen wrote:
> On Wed, 19 Aug 2015 22:52:52 +0300, Evgeny Filatov > <e.v.filatov@ieee.org> wrote: > >> On 18.08.2015 21:29, gyansorova@gmail.com wrote: >> (snip) >> >>> Just a small correction, sampling theory was not due to Nyquist and Shannon but Whittaker and a Russian gentleman. Shannon just put it in an engineering framework. >>> >> >> That gentleman's name is Kotelnikov. >> >> http://en.wikipedia.org/wiki/Vladimir_Kotelnikov >> >> Evgeny. >> > > It's sad that the cold war kept a lot of science and engineering > developments of the two sides separated for so long. I hope that > doesn't ever happen again. > > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com >
Actually one of the reasons I like this place is that it's apolitical. A decade ago, when I was a college student, once we've got the attention of a "telephone terrorist". There was a phone call to the police (falsely) claiming there's a bomb somewhere in the college. All classes were cancelled. Except for, guess what? A lecture in calculus, which went on like if nothing extraordinary had happened. Imho, that tells something about the relative importance of math and politics. Evgeny.
Evgeny Filatov wrote:
> On 19.08.2015 23:51, Eric Jacobsen wrote: >> On Wed, 19 Aug 2015 22:52:52 +0300, Evgeny Filatov >> <e.v.filatov@ieee.org> wrote: >> >>> On 18.08.2015 21:29, gyansorova@gmail.com wrote: >>> (snip) >>> >>>> Just a small correction, sampling theory was not due to Nyquist and >>>> Shannon but Whittaker and a Russian gentleman. Shannon just put it >>>> in an engineering framework. >>>> >>> >>> That gentleman's name is Kotelnikov. >>> >>> http://en.wikipedia.org/wiki/Vladimir_Kotelnikov >>> >>> Evgeny. >>> >> >> It's sad that the cold war kept a lot of science and engineering >> developments of the two sides separated for so long. I hope that >> doesn't ever happen again. >> >> >> Eric Jacobsen >> Anchor Hill Communications >> http://www.anchorhill.com >> > > Actually one of the reasons I like this place is that it's apolitical. > > A decade ago, when I was a college student, once we've got the attention > of a "telephone terrorist". There was a phone call to the police > (falsely) claiming there's a bomb somewhere in the college. All classes > were cancelled. Except for, guess what? A lecture in calculus, which > went on like if nothing extraordinary had happened. > > Imho, that tells something about the relative importance of math and > politics. > > Evgeny. >
It may also tell us that those who teach calculus may have a better grasp on probability than other people. -- Les Cargill
On Friday, August 21, 2015 at 9:30:47 AM UTC-4, kaz wrote:
> >Hi, > > > > If I have a sine wave with period T. The sampling theory says I can > >recover it by sampling at T/2. That is two points, barely enough to draw > a > >straight line. > > > > What am I missing here? > > > > > >--------------------------------------- > >Posted through http://www.DSPRelated.com > > There is plenty of response to your post. I don't see any issue here. > if you are in digital domain and have two regular values into a DAC device > then you can construct the sine wave (after filtering images). > If you are in analogue domain you can sample a sine waveform by two > samples per period, best SNR occurs if you hit the peaks/troughs and zero > occurs if you hit at zero crossings. anywhere in between can be > interpolated back for better snr. > > so why two points mean a straight line? > > Kaz > --------------------------------------- > Posted through http://www.DSPRelated.com
This is not correct. If you sample at 2 samples per period for a sinusoidal waveform, the values are of the form -V, +V, for V>=0. You cannot know the amplitude of the of the sinusoid since the samples could have come from a sinusoid with ANY amplitude >= V. If V=0, you do not even know of a sinusoid is present from the samples. In general you do not know the phase. The exception is when V=0, if you know a sinusoid is actually present (which you can't tell from the samples). Dirk