# Nyquist Didn't Say That

Started by August 22, 2006
```Jerry Avins wrote:

> In theory only. To resolve a signal at 2.00000X would require 1,000,000
> seconds. (OK: maybe only 150 hours.)

150 hours? Why?

> Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10
> Hz, you also need to to sample for a time in the order of 1/10 second.
> Why does it seem strange?
>
1/f is twice the nyquist time (1/2 the rate, undersampling) yet you
seem to be implying oversampling

```
```Tim Wescott wrote:
> Oli Filth wrote:
>
> > Tim Wescott said the following on 22/08/2006 23:23:
> >
> >> The misconceptions that I noticed pretty much boiled down to the
> >> following two:
> >>
> >> One, "I need to monitor a signal that happens at X Hz, so I'm going to
> >> sample it at 2X Hz".
> >>
> >> Two, "I can sample at X Hz, so I'm going to build an anti-alias filter
> >> with a cutoff of X/2 Hz".
> >
> >
> > Are you referring to:
> >
> > a) bandpass sampling,
>
> I doubt that I'm going to touch bandpass sampling, and if I do it'll be
> using a 10 foot pole.
>
> > or
> > b) in baseband sampling, the notion that in practice, one needs to
> > sample faster than 2X Hz to measure something at X Hz?
> >
> Yes, (b).  As well as the notion that just because your signal has a
> fundamental frequency of X that doesn't mean it doesn't have harmonics
> up as far as the imagination can reach.

but, Tim, the point is that you have to sample *faster* than 2X.
sampling at 2X ain't good enough, even theoretically.  sampling at
2.000001X might be good enough theoretically (the reconstruction filter
will be a bitch) if acausality (or a long delay for the causal case)
ain't a problem.  the other thing to think about is that no D/A really
outputs dirac impulses, so then something like a zero-order hold (ZOH)
might have to be modeled for reasons of practicallity.

lastly, even though we fight about a bunch of other things, i was
surprized at the support i had at Wikipedia to include that "T factor"
in the dirac comb sampling operator.  putting it there and not in the
passband gain of the reconstruction filter is dimensionally most
appropriate and help set up the ZOH model without dropping the T factor
(or going through a contorted argument for how to include it).

am repeating someone else's words.

r b-j

```
```Jim Stewart wrote:
>
> Before going into a detailed article, perhaps
> you could review/improve the wikipedia article:
>
> http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem

i just came upon this.  as one who has recently jumped into that fray,
alls i can say is "HELP!".

even if you lock horns with me, i would really like it if more
comp.dspers would come to Wikipedia and contribute.  someday, that can
be the new FAQ, for *any* newsgroup.

r b-j

```
```robert bristow-johnson wrote:
>
... snip ...
>
> but, Tim, the point is that you have to sample *faster* than 2X.
> sampling at 2X ain't good enough, even theoretically.  sampling at
> 2.000001X might be good enough theoretically (the reconstruction
> filter will be a bitch) if acausality (or a long delay for the
> causal case) ain't a problem.  the other thing to think about is
> that no D/A really outputs dirac impulses, so then something like
> a zero-order hold (ZOH) might have to be modeled for reasons of
> practicallity.

There is a world of difference between the output filters needed
after a sample and hold, and after a quasi impulse function.  Also
in the gain needed.

The impulse function has the advantage that several can be mixed.
I took advantage of this in a PABX years ago to provide call
merging.  The actual pulses were about 1% of the repetition rate
period.  The accumulated DC components limited the merging to three
calls.

--
Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net)
Available for consulting/temporary embedded and systems.

```
```bungalow_steve@yahoo.com wrote:
> Jerry Avins wrote:
>
>> In theory only. To resolve a signal at 2.00000X would require 1,000,000
>> seconds. (OK: maybe only 150 hours.)
>
> 150 hours? Why?

A bad assumption on my part. 2.000001X isn't Hz; it needs to be
normalized. The result is not a million seconds, but a million sample
times. That's still a long time. Most of the time, there's pretty good
resolution at half that, in this case, 500,000 sample times.

>> Right or wrong, that's what I meant.* What's more, to resolve Fs/2 - 10
>> Hz, you also need to to sample for a time in the order of 1/10 second.
>> Why does it seem strange?
>>
> 1/f is twice the nyquist time (1/2 the rate, undersampling) yet you
> seem to be implying oversampling

I don't see what you mean. Could you explain with an equation or two?

Jerry
--
Engineering is the art of making what you want from things you can get.
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```
```Jonathan Kirwan wrote:

>     ...  You need some margin for the skirts, don't you?

If course, and for other things too. Even if you can be certain that
there is no signal energy above Fmax, you need to sample faster than
2Fmax in real situations. As it says on traffic a summons in Boston,
"Fail ye not thereof at your peril."

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```Eric Jacobsen wrote:

>    ...   You really only need to sample 2x the
> bandwidth, as Nyquist stated, and in the case of something like a
> square wave one must determine the "bandwidth of interest", i.e., some
> point above which you're not interested or it won't matter.

C'mon, Eric; I know you know better.  Either you sample so fast that
significant aliases are higher than any component of interest (and so
can be filtered digitally later) or you use an anti-alias filter so that
in fact there's nothing to alias.

> For sampled-IF (or super-Nyquist as some call it), one must pay
> attention to folding frequencies, etc.

Calling it "super Nyquist" reveals the ignorance that underlies the problem.

> It's not hard to sort out, but I think an article like what is
> proposed is always a good thing, if well written, to clarify things
> and help folks avoid the pitfalls.

Ja!

Jerry
--
Engineering is the art of making what you want from things you can get.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
```
```"robert bristow-johnson" <rbj@audioimagination.com> wrote in

> http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
>
> i think there is some writing that craps up the article, but that is
> the lot and legacy of Wikipedia.  an encyclopedia written by committee
> (the biggest, most inclusive committee possible).  so "design by
> committee" is a problem.
>
>> Danke.
>
> Bitte.
>
> r b-j
>
>

Robert--

CommitteeSize = CommitteeSize + 1  ; %!!!!!

I think what's missing is a demonstration that multiplication with the
Dirac train in time pairs with convolution with the scaled Dirac in
frequency.  Without a good figure showing that, the figures under the
"aliasing" subtitle lack some meaning.

As an aside, I'm interested in the analogs in AM.  By the book, the
carrier needs to be twice as fast as the highest signal component, but
for Hilbert demodulation, all I can find is the specification that the
signal and carrier not overlap.  Is this because the transform
essentially throws out the negative frequencies, so you don't have to
worry about positive/negative overlap?  Alternatively, am I just wrong,
and the carrier needs to be twice the highest frequency, even for Hilbert
demod??

--
Scott
```
```On Wed, 23 Aug 2006 17:15:17 -0400, Jerry Avins <jya@ieee.org> wrote:

>Eric Jacobsen wrote:
>
>>    ...   You really only need to sample 2x the
>> bandwidth, as Nyquist stated, and in the case of something like a
>> square wave one must determine the "bandwidth of interest", i.e., some
>> point above which you're not interested or it won't matter.
>
>C'mon, Eric; I know you know better.  Either you sample so fast that
>significant aliases are higher than any component of interest (and so
>can be filtered digitally later) or you use an anti-alias filter so that
>in fact there's nothing to alias.

What I had in mind was either that there's natural filtering going on
via bandlimiting of the media (even traces on a circuit board are
bandlimited), or you've limited your "area of interest" via suitable
filtering.

Even allowing low-power aliasing into high frequencies is okay if it's
outside of the "area of interest" and one is going to take care of it
via digital filtering.

Pointing out the effects of aliasing would be fundamental in such an
article, so I assuming that was assumed.   Hmmm...a second order
assumption.   That must be where I went wrong...  ;)

>> For sampled-IF (or super-Nyquist as some call it), one must pay
>> attention to folding frequencies, etc.
>
>Calling it "super Nyquist" reveals the ignorance that underlies the problem.

As long as it's understood what is meant I don't mind the term.   I've
not heard it used ambiguously, so I suppose we're stuck with it.   I
hear it fairly commonly although I do refrain from using it unless
present company uses it first...gotta speak the language of the
locals.

>> It's not hard to sort out, but I think an article like what is
>> proposed is always a good thing, if well written, to clarify things
>> and help folks avoid the pitfalls.
>
>Ja!
>
>Jerry
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org
```
```Jerry Avins wrote:
> steve wrote:
-- snip --

>
> So many misconceptions, so little time. Tim: are you tuned in?
>
Yes I am, and this discussion is great.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com