Nyquist Didn't Say That

David Hearn wrote:
> Tim Wescott 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.
>
> So, if you need to monitor a signal that occurs at xHz - what frequency
> should you sample it at?
>
> D

a little over 2x the bandwidth of the signal should be sufficient,

-Lasse

Jim Stewart wrote:

> Tim Wescott 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?
> 
> 
> Before going into a detailed article, perhaps
> you could review/improve the wikipedia article:
> 
> http://en.wikipedia.org/wiki/Nyquist-Shannon_sampling_theorem
> 
> 
Because I'm a mercenary.

Posting to wikipedia doesn't pay directly, nor does it give me public 
credit.  While it benefits the world it doesn't lead to me getting any 
checks in the mail.

By contrast I can contribute to newsgroups, post articles on my website, 
or sell articles to trade magazines.  Each one of these activities binds 
my name to the knowledge*, gives it distribution to the english speaking 
world to one extent or another, gives me a reasonable chance of having 
my name pop up on a web search, and should it get bought by a magazine 
I'll get almost 1/10th of minimum wage for the effort I've put into it. 
  As a consequence, folks who need to know how to do the stuff I write 
about see me as a potential resource when they go looking for consultants.

Until I win the lottery or retire I can't afford to spend the time on 
anonymous contributions to Wikis.

* Hopefully that's a good thing.

-- 

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

Posting from Google?  See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim,

"Tim Wescott" <tim@seemywebsite.com> wrote in message 
news:hrGdnX1RNLcIE3bZnZ2dnUVZ_omdnZ2d@web-ster.com...
> Posting to wikipedia doesn't pay directly, nor does it give me public 
> credit.  While it benefits the world it doesn't lead to me getting any 
> checks in the mail.

Perhaps you'd be willing to take your articles and post them on Wikipedia as 
well as the places where your name is directly tied to it (in a slightly 
modified form)?  That way you'd help the public at large (it's a lot easier to 
find things on Wikipedia than trying to search through a dozen technical 
journals), and anyone who actually *has* money to pay will still find you.

---Joel

langwadt@ieee.org wrote:
> David Hearn wrote:
> > Tim Wescott 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.
> >
> > So, if you need to monitor a signal that occurs at xHz - what frequency
> > should you sample it at?
> >
> > D
>
> a little over 2x the bandwidth of the signal should be sufficient,

Depending on what you want to do. And you'd better make sure that your
sampling points aren't 180 degrees apart wrt to the signal frequency
you want to sample.

--
Bill Sloman, Nijmegen

Joel Kolstad wrote:

> Tim,
> 
> "Tim Wescott" <tim@seemywebsite.com> wrote in message 
> news:hrGdnX1RNLcIE3bZnZ2dnUVZ_omdnZ2d@web-ster.com...
> 
>>Posting to wikipedia doesn't pay directly, nor does it give me public 
>>credit.  While it benefits the world it doesn't lead to me getting any 
>>checks in the mail.
> 
> 
> Perhaps you'd be willing to take your articles and post them on Wikipedia as 
> well as the places where your name is directly tied to it (in a slightly 
> modified form)?  That way you'd help the public at large (it's a lot easier to 
> find things on Wikipedia than trying to search through a dozen technical 
> journals), and anyone who actually *has* money to pay will still find you.
> 
> ---Joel
> 
> 
I may do that.

-- 

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

Posting from Google?  See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott wrote:



>>> 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?

Recently I run into a problem with the digital PLL occasionally locking 
on the aliased frequencies. The problem happens when the signal 
constellation has N phase angles. That multiplies the difference phase 
by N. Thus the error frequency may appear to be higher then baudrate/2, 
causing all kinds of problems. Special care has to be taken to avoid this.



Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Tim Wescott <tim@seemywebsite.com> wrote in 
news:q6mdnZgxjJhQHnbZnZ2dnUVZ_rGdnZ2d@web-ster.com:

> 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?
> 

Leave plenty of headroom is the motto.  These days, with disk space 
around a buck per Gig, and communication protocols that sling data from 
embedded systems to where they need to be very quickly, sample faster 
than you need to.  Having a sample rate that's too fast could cause 
problems with digital filter design down the road a ways, but it a 
helluva lot easier to downsample later then to find out later you haven't 
sampled fast enough and lost data integrity.  If it's important, filter 
if you need to.  For about $100/channel, you can get nifty 8-pole Bessels 
that have pretty linear phase in the pass band.  Personally, Im big on 
anti-aliasing filtering.  I do pretty low frequency physiological stuff, 
and by matter of course I filter with 8 poles at 200Hz and sample at 500.  

But, people should be aware that anti-aliasing filtering is no magic 
bullet, and can be worthless if you design something wrong, like if you 
introduce ground loops or somehow push noise into the system after the 
filters.  Anti-aliasing countermeasures begin with careful analog design 
to keep high frequency noise out of the system-- shields, good grounding 
schemes, correct bypassing, etc.  Even with care, this can get nasty if 
you're driving real loads, like motors.  I've toyed around with the 
whacked out idea of entirely isolating data acquisition and prefiltering 
from everything else, with isolating DC/DC converter or isolation 
transformers, and linear optical isolators on every analog input or 
output, and plain old optical isolators on every digital line.  This 
design got expensive quickly, and its almost guaranteed to fail when 
someone new tries to expand your system.

The more headroom in Nyquist you can afford to have, the less money 
you'll need to spend on your anti-aliasing filters, because the rolloff 
can be more gentle--sort of like how oversampling digital music makes the 
output filter cheaper.  The choice of filter family is also a design 
parameter that might depend on good ol' Nyquist.  If you're keeping 
things loose, you can choose a filter that doesn't drop like a hot rock, 
like a Bessel or Butterworth, but if you need to tighten things up, you 
need a Chebyshev or some such.  


That brings up another issue:  anti-alias filtering is not free--clearly 
from a cost perspective, but you also need to deal with time delays and 
small passband gain fluctuation for Bessel Filters, passband phase 
distortion problems for Butterworth (and maybe a lower cutoff frequency 
to help with the slow rolloff), and phase and gain problems for the 
chebyshevs, when you need really fast rolloffs.


I've also thought about actually doing silly things, like using dsp's to 
sample superfast with cheap analog filters on the inputs, and then doing 
the real filtering digitally, spitting the results out on DACs, and then 
resampling for storage.  This seems real odd, but push comes to shove, it 
might be cheaper than $100 per channel for good analog filters.  But, it 
doesn't really make sense-- you could just use the base system to 
oversample like mad, filter, and decimate prior to storage.

Sorry for the ramble, Tim.  It's a little late for me to be forming 
replies like this.




-- 
Scott
Reverse name to reply

Tim Wescott 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".
>


Nyquist said that you need to sample at least 2X Bandwidth of the
signal to accurately reconstruct that signal. This is often miss-quoted
because in control system or some  other applications the bandwidth
goes down to dc so we are quote 2X highest freq of interest.

Of course due to other problems (not going into them here) we need to
sample about 5 to 10 times higher where feedback is involved.

S.

*** top posting fixed ***
decious wrote:
> Tim Wescott wrote:
>> David Hearn wrote:
>>> Tim Wescott wrote:
>>>
>>>> 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?
>>>
>>> So, if you need to monitor a signal that occurs at xHz - what
>>> frequency should you sample it at?
>>
>> You need to be more than 2X times the highest interesting
>> frequency component in your periodic wave, which can be quite
>> high in some cases.  You may also have to do some anti-alias
>> filtering.
>>
>> Or in other words "that depends".  Which is why I'm writing the
>> dang article, so I only have to write it once...
> 
> are you going to be including in your artcle cases with filter
> banks, specifically, critical sampled, oversampled etc, and how
> nyquist fits into those implementations?

Don't top-post.  It is rude and contravenes the standard practices
in newsgroups.  Your response belongs below, or intermixed with,
the *snipped* material you quote.  See the links in my sig. below.

The thing to remember about alias filtering is the word alias.  The
point is to remove incoming signals that can create false, or
alias, signals in the output.  No alias filter can really be an
instantaneous cutoff, so you have to ensure that aliasing noise is
sufficiently attenuated to not affect the actual response.  At the
same time all filters have effects on the time delay at various
frequencies, or phase response.  Linear phase filters, or constant
delay filters, have much less sharp cutoffs than may be desirable.

As ever, the task of the engineer is to make suitable compromises
between performance and cost.  There is nothing magic about the
word Nyquist - it is purely a theoretical limit.

I imagine these are the sort of things Tim will address.

Read the links below, and please refrain from top-posting in the
future.  It will make life easier for all.

-- 
 Some informative links:
   news:news.announce.newusers
   http://www.geocities.com/nnqweb/
   http://www.catb.org/~esr/faqs/smart-questions.html
   http://www.caliburn.nl/topposting.html
   http://www.netmeister.org/news/learn2quote.html

Tim Wescott 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.

A couple of others have mentioned this already, but the bandwidth vs
highest frequency issue does come to mind.

Rune