Implications of Nyquist? ?????

Started by Richard Owlett May 17, 2009
_TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to 
sample a waveform at >= a particular frequency.

I've gut feeling that Nyquist implies more.

I suspect it's more about information transfer rate.

What question should I be asking.

Signed
ADMITTED *STUPIDENT*

On May 17, 3:38&#2013266080;pm, Richard Owlett <rowl...@atlascomm.net> wrote:
> _TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to > sample a waveform at >= a particular frequency. > > I've gut feeling that Nyquist implies more. > > I suspect it's more about information transfer rate. > > What question should I be asking. > > Signed > ADMITTED *STUPIDENT*
It's a sufficient condition, but it's not necessary. For example, you can look at recent work on sampling at the "rate of innovation" of a signal. It does not say anything about the distribution of parameters, however, so it's not as simple as translation to "information rate". http://lcavwww.epfl.ch/research/topics/sampling_FRI.html
On Sun, 17 May 2009 14:38:33 -0500, Richard Owlett wrote:

> _TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to > sample a waveform at >= a particular frequency. > > I've gut feeling that Nyquist implies more. > > I suspect it's more about information transfer rate. > > What question should I be asking. > > Signed > ADMITTED *STUPIDENT*
The Nyquist-Shannon sampling theorem is, when you get right down to it, _highly_ theoretical, in that it sets you the impossible condition of an absolutely band limited signal. You can't perfectly band limit a real- world signal, so if you're working with real-world systems the Nyquist- Shannon sampling theorem doesn't "really" apply. The Nyquist rate does make a nice line in the sand that you can draw, and compare what you're doing with Nyquist, either by information content vs. the Nyquist rate or the Nyquist rate vs. the highest "significant" frequency. My preferred method for understanding all of this is to understand how a sampler aliases a signal, and work from there. When you do that the Nyquist rate is there, but you're not trying to directly draw conclusions from it: http://www.wescottdesign.com/articles/Sampling/sampling.html. -- www.wescottdesign.com
Tim Wescott <tim@seemywebsite.com> wrote:
 
< The Nyquist-Shannon sampling theorem is, when you get right down to it, 
< _highly_ theoretical, in that it sets you the impossible condition of an 
< absolutely band limited signal.  You can't perfectly band limit a real-
< world signal, so if you're working with real-world systems the Nyquist-
< Shannon sampling theorem doesn't "really" apply.

Not only absolute band limited but infinite duration.  
 
< The Nyquist rate does make a nice line in the sand that you can draw, and 
< compare what you're doing with Nyquist, either by information content vs. 
< the Nyquist rate or the Nyquist rate vs. the highest "significant" 
< frequency.
 
< My preferred method for understanding all of this is to understand how a 
< sampler aliases a signal, and work from there.  When you do that the 
< Nyquist rate is there, but you're not trying to directly draw conclusions 
< from it:  http://www.wescottdesign.com/articles/Sampling/sampling.html.

I suppose that works.  I usually consider that besides sampled real
world signals are also quantized, and if you get below the quantization
noise you are doing about as well as you can do.  It is convenient
of the human aural system to have a nice cutoff frequency.  (More 
or less, depending on age.)

-- glen
 
On May 18, 10:55&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> On Sun, 17 May 2009 14:38:33 -0500, Richard Owlett wrote: > > _TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to > > sample a waveform at >= a particular frequency. > > > I've gut feeling that Nyquist implies more. > > > I suspect it's more about information transfer rate. > > > What question should I be asking. > > > Signed > > ADMITTED *STUPIDENT* > > The Nyquist-Shannon sampling theorem is, when you get right down to it,
You mean the Whittaker-Shannon-Kotelnikov Sampling Theorem. Hardy
On May 17, 9:46&#2013266080;pm, HardySpicer <gyansor...@gmail.com> wrote:
> On May 18, 10:55&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote: > > > On Sun, 17 May 2009 14:38:33 -0500, Richard Owlett wrote: > > > _TYPICALLY_ when looking to satisfy "Nyquist criterion" one looks to > > > sample a waveform at >= a particular frequency. > > > > I've gut feeling that Nyquist implies more. > > > > I suspect it's more about information transfer rate. > > > > What question should I be asking. > > > > Signed > > > ADMITTED *STUPIDENT* > > > The Nyquist-Shannon sampling theorem is, when you get right down to it, > > You mean the Whittaker-Shannon-Kotelnikov Sampling Theorem. > > Hardy
To be precise, Raabe-Whittaker-Shannon-Kotelnikov? Except that Raabe wrote his thesis in the wrong country (Germany), in the wrong university (Technical University of Berlin), at the wrong time (1938) ;-). Julius
On Sun, 17 May 2009 23:02:45 +0000, glen herrmannsfeldt wrote:

> Tim Wescott <tim@seemywebsite.com> wrote: > > < The Nyquist-Shannon sampling theorem is, when you get right down to > it, < _highly_ theoretical, in that it sets you the impossible condition > of an < absolutely band limited signal. You can't perfectly band limit > a real- < world signal, so if you're working with real-world systems the > Nyquist- < Shannon sampling theorem doesn't "really" apply. > > Not only absolute band limited but infinite duration.
If I am not mistaken an absolutely band limited signal _is_ of limited duration, which is one of the salient features that makes it impossible to be real world.
> < The Nyquist rate does make a nice line in the sand that you can draw, > and < compare what you're doing with Nyquist, either by information > content vs. < the Nyquist rate or the Nyquist rate vs. the highest > "significant" < frequency. > > < My preferred method for understanding all of this is to understand how > a < sampler aliases a signal, and work from there. When you do that the > < Nyquist rate is there, but you're not trying to directly draw > conclusions < from it: > http://www.wescottdesign.com/articles/Sampling/sampling.html. > > I suppose that works. I usually consider that besides sampled real > world signals are also quantized, and if you get below the quantization > noise you are doing about as well as you can do. It is convenient of > the human aural system to have a nice cutoff frequency. (More or less, > depending on age.)
Yup. Although you may get into the "I just don't care about noise here for this application" before you get into quantization noise. -- http://www.wescottdesign.com
Tim Wescott wrote:

   ...

> If I am not mistaken an absolutely band limited signal _is_ of limited > duration, which is one of the salient features that makes it impossible > to be real world.
Erm .. unlimited duration? ... Jerry -- Engineering is the art of making what you want from things you can get. &macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;&macr;
On May 17, 9:22&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On Sun, 17 May 2009 23:02:45 +0000, glen herrmannsfeldt wrote: > > Tim Wescott <t...@seemywebsite.com> wrote: > > > If I am not mistaken an absolutely band limited signal _is_ of limited > duration, which is one of the salient features that makes it impossible > to be real world.
That is, the signal is limited in **both** frequency and time? I don't believe that this is correct. A signal that is absolutely limited in one domain extends to plus/minus infinity in the other domain. A strictly band-limited signal is of infinite duration, and a strictly time-limited signal has Fourier transform that is nonzero for arbitrarily large values of frequency. --Dilip Sarwate
Tim Wescott <tim@seemywebsite.com> wrote:
 
> Yup. Although you may get into the "I just don't care about noise here > for this application" before you get into quantization noise.
Well, that does happen. I have discussed here before 24 bit WAV recordings in an auditorium full of kids. The background noise is definitely higher than the quantization noise. In one, in addition they had a PA system on with a noticable hum, and then there is the ventilation system. -- glen