# Implications of Nyquist? ?????

Started by 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

```
```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

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

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
>
> 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
>
> > 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.
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```
```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
```