Nyquist Didn't Say That

Robert Baer wrote:
> Stef wrote:
>
> > In comp.arch.embedded,
> > mobi <mobien@gmail.com> wrote:
> >
> >>Do consider this interesting (atleast for me) example
> >>
> >>Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> >>i start sampling from time = 0. What would i get? Aint i statisifying
> >>Nyquist here?
> >
> >
> > No you are not. You seemed to have missed Rune's post in this thread
> > about '=' vs ' >'.
> >
> >
> ...then re-state with sampling at 2X+delta where delta is (say) 1Hz!


As mentioned earlier, the information rate about a sampled waveform is
proportional to the rate above the 2x limit. If you sample at 2.5 the
highest frequency iof interest (speaking in a bandwidth sense), you
will get sufficient information about said signal faster than if you
sample at 2.1x.

That obviously impacts the reconstruction filter (as has also been
mentioned). I seem to recall (it's been a long time, but makes sense)
that the time required to properly train to a reconstructed signal is
inversely proportional to the normalised sample rate above the 2x
limit.

This may seem obvious, but as noted a lot of people don't think through
the effect of the sampling or the theory behind it. If I sample at
2.1x, I need more full output cycles at the x rate for full
reconstruction than I would need if I sampled at 2.5x.

My rule of thumb is to sample at 2.5x at a minimum . There are times I
sample at 10x or more. A number of people want a fixed answer for all
applications, where there isn't any such panacea. 'It depends' is
probably the most common engineering term ;)

Something else that might be usefully mentioned in this context is the
ADC type used at the input - a Delta Sigma converter inherently
decimates the signal, reducing the requirements on the front end
anti-aliasing filter. A SAR gives no such assistance. The same
consideration of DAC type might also be useful.

Cheers

PeteS

PeteS wrote:
> 
... snip ...
> 
> This may seem obvious, but as noted a lot of people don't think
> through the effect of the sampling or the theory behind it. If I
> sample at 2.1x, I need more full output cycles at the x rate for
> full reconstruction than I would need if I sampled at 2.5x.
> 
> My rule of thumb is to sample at 2.5x at a minimum . There are
> times I sample at 10x or more. A number of people want a fixed
> answer for all applications, where there isn't any such panacea.
> 'It depends' is probably the most common engineering term ;)

In the PABX telephony example I gave earlier, we initially sampled
at 10 kHz to get essentially flat response to 3.5 kHz with constant
delay.  We upped the sample rate to 12 kHz later to ease the
requirements on the filters and equalization.

-- 
Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net)
   Available for consulting/temporary embedded and systems.
   <http://cbfalconer.home.att.net> USE maineline address!

On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com>
wrote:

>Kinda off topic --
>
>A month or two ago there was a spate of postings on these groups 
>displaying a profound misunderstanding of how to apply Nyquist's theorem 
>to problems of setting sampling or designing anti-alias filters.  I 
>helped folks out as much as I could, but it really demands an article, 
>which I am currently working on.
>
>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".
>
>I estimate that answering these misconceptions will only take 3-4k 
>words, but I don't want to miss any other big ones.
>
>Have you seen any other real howlers that relate to Nyquist, and what 
>you should really be thinking about when you're pondering sampling 
>rates, anti-aliasing filters and/or reconstruction filters?
>
>Danke.
>Tim Wescott
>Wescott Design Services



Hi Tim,
   
   Writing about the effects of "periodic sampling" 
is an interesting and educational thing to do.

My guess is that you'll have to address the controversial 
notion of "negative frequency", as well as why it 
is valid to show spectral replications (spaced 
Fs hertz apart) when we draw a freq-domain picture 
of the spectrum of a discrete (digital) signal.

One interesting aspect of periodic sampling is that 
it's easy to misinterpret the results of software 
modeling of the process of periodic sampling.

That's (I think) what happened when J. L. Smith wrote 
his "Breaking the Nyquist Barrier" in the July 1995 
issue of the IEEE Sig. Processing magazine.
I believe Smith misunderstood his software-generated 
plots when he wrote his embarrassing article.
Smith claimed that he could violate the Nyquist 
Theorem and not lose any information (and 
avoid any ambiguous information) regarding some 
time domain signal.  Smith's article resulted in a 
flurry of "Letters To the Editor" that debunked 
the article (See the Nov. 1995, Jan. 1996, and 
the May 1996 issues for examples of the letters.)
How embarrassing that must have been 
for both Smith, and the Editors of the magazine who 
should have known better.

Another very "misguided" sampling article was 
"Apply Fundamentals To Avoid Surprises With 
Sampled Systems" written by Gerard Fonte and 
printed in the June 24th 1993 issue of EDN magazine. 
Fonte also claimed that you could violate 
Nyquist and not lose any information.
Almost every paragraph of that article contains 
misconceptions and ambiguities regarding the 
Nyquist sampling theorem.  It's truly a "ghastly" 
article --- and it also caused a deluge of 
"Letters To the Editor" pointing out all the 
errors in the article.  (See page 25 of the 
Sept. 30th 1993 issue of the EDN magazine 
for example.)

I thought after all the criticism that Fonte 
received regarding his 1993 EDN that we'd 
heard the last from Mr. Fonte.   Not so.
He wrote another titled "Breaking Nyquist" 
in the October 1998 issue of the Circuit Cellar 
magazine.  Again he claimed that the 
Nyquist sampling theorem is not valid 
and that it can be "broken" without 
causing "problems".   Using vague, ambiguous, 
undefined terminology, Fonte again claimed that 
he can tell the difference between an Fo 
(F sub zero) discrete spectral component of 
an analog sinewave whose Fo frequency was less 
than Fs/2 and an Fo discrete spectral component 
of an aliased analog sinewave whose frequency was 
greater than Fs/2.  In other words, he claims that 
"aliasing" (violating Nyquist) does NOT cause 
spectral ambiguity in the frequency domain.
I can hardly wait for Fonte's next article.

(I'm not being hateful here...Fonte's probably 
a nice guy whom his family loves.)

My guess is, again, Fonte is using software to 
model the process of periodic sampling, and the 
signal he is "sampling" is a pure sinewave.
Such modeling is very risky in my opinion because 
it's easy for a beginner in the field of 
DSP to misinterpret/misunderstand the results 
of such modeling. 

Concerning sampling, Bonnie Baker wrote an 
article titled "Turning Nyquist Upside Down 
by Undersampling" in the May 12th 2005 issue 
of EDN magazine.  The article discusses bandpass 
sampling.  However, I think the article's 
title is unfortunate because bandpass 
sampling does NOT "turn Nyquist upside down"
---bandpass sampling is included in the Nyquist 
Sampling Theorem.

I tell the students in my DSP class that,
"Periodic Sampling is one of the most 
misunderstood topics in DSP."  I think I'm 
justified in making that claim.

Hey Tim,
I think in any dissertation on "sampling" it 
would be a good idea to discuss bandpass sampling.
Bandpass sampling is not only an interesting topic, 
but it's a very 
practical topic in these days of digital 
communications.  (Just my two cents.)

See Ya',
[-Rick-]

On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com>
wrote:

>Kinda off topic --
>
>A month or two ago there was a spate of postings on these groups 
>displaying a profound misunderstanding of how to apply Nyquist's theorem 
>to problems of setting sampling or designing anti-alias filters.  I 
>helped folks out as much as I could, but it really demands an article, 
>which I am currently working on.
>
  (snipped)

Hi,
  I just finished posting a long rant 
about sampling articles written by Gerard Fonte.

I just noticed (on the web) that the San 
Fernando Valley Engineers' Council Inc.
has awarded Gerard Fonte an "Outstanding 
Engineering Achievement Merit Award" for 2006.

See:
http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4

[-Rick-]

Another issue,
Isnt it important to always keep into mind what the recustruction
filter is?

Lets consider this situation.
I have an output signal from a  ZOH. I want to sample it again and
reconstruct it back. Now i think i need only one sample per ZOH symbol.
Why? Cos my reconstruction filter can construct my signal exactly from
one sample. Certainly i am not satisfying Nyquist in this case. Or
maybe i have not been sleeping to well :o)


Jerry Avins wrote:
> 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.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

Robert Baer wrote:
> 
> mobi wrote:
> 
> > Do consider this interesting (atleast for me) example
> >
> > Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
> > i start sampling from time = 0. What would i get? Aint i statisifying
> > Nyquist here?
> >
>
> >
>    Yup!
>    Also try sampling at a constant delay from the sine zero crossing.
>    That is what happens when people blindly follow a "criteria" without
> knowing the full reason and background.

What is what happens? Do you actually know what happens if you actually
try this in a real world context? Set up a speaker generating the Fs/2
signal. Set up a microphone and and ADC to record the sound at Fs. Are
you claiming that you can adjust the sampling phase to produce a digital
recording of either full scale or zero? That's what in theory should
happen - right? But can you do that in real life?

-jim

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Rick Lyons wrote:
[...]
> Hey Tim,
> I think in any dissertation on "sampling" it 
> would be a good idea to discuss bandpass sampling.
> Bandpass sampling is not only an interesting topic, 
> but it's a very 
> practical topic in these days of digital 
> communications.  (Just my two cents.)

And complex sampling. You must include that, otherwise people won't 
understand the solid unshakeable reality of negative frequencies. :-)

Regards,
Steve

Tim Williams <tmoranwms@charter.net> wrote:

> FOAD.  It was a short, to-the-point comment.  The only possible rational
> argument that can be made to his post is that he didn't trim the quoted
> text.

The only possible rational argument? You really are a complete fucking
moron.


Tim

Rick Lyons wrote:

> Hi,
>   I just finished posting a long rant
> about sampling articles written by Gerard Fonte.
>
> I just noticed (on the web) that the San
> Fernando Valley Engineers' Council Inc.
> has awarded Gerard Fonte an "Outstanding
> Engineering Achievement Merit Award" for 2006.
>
> See:
> http://engineerscouncil.org/Gallery/EWeekBanquet2006?page=4

It has been my experience with local engineers' groups that the people
who get awards are the ones who show up regularly.

jim wrote:
> 
> Robert Baer wrote:
>> mobi wrote:
>>
>>> Do consider this interesting (atleast for me) example
>>>
>>> Consider pure Sin wave at X Hz. I start sample it at 2X. Unfortunately
>>> i start sampling from time = 0. What would i get? Aint i statisifying
>>> Nyquist here?
>>>
>>    Yup!
>>    Also try sampling at a constant delay from the sine zero crossing.
>>    That is what happens when people blindly follow a "criteria" without
>> knowing the full reason and background.
> 
> What is what happens? Do you actually know what happens if you actually
> try this in a real world context? Set up a speaker generating the Fs/2
> signal. Set up a microphone and and ADC to record the sound at Fs. Are
> you claiming that you can adjust the sampling phase to produce a digital
> recording of either full scale or zero? That's what in theory should
> happen - right? But can you do that in real life?

Of course you can lock the sampler to the sampled waveform or one of its 
harmonics. Google for "PLL".

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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