Nyquist Didn't Say That

Vladimir Vassilevsky wrote:
> 
> 
> 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.

Isn't that just the generic issue that after sampling you'd better make 
sure your algorithms don't result in any frequency multiplication? If 
they do, you'll fatten the bandwidth and be in trouble.

Regards,
Steve

You should discuss the question of whether it is possible to remove 
unwanted aliased-in noise by clever digital filtering in a downstream 
calculation.  In my understanding this is not possible.  But maybe I 
slept through that part of the class.

You should discuss what happens to a signal that is filtered and sampled 
in one system at rate X, but is transmitted to a receiving system at 
update rate Y, then used by that receiving system at rate Z.  How should 
one select the analog anti-aliasing filter in this situation?

mw

On Tue, 22 Aug 2006 23:31:53 +0100, David Hearn <dave@NOswampieSPAM.org.uk>
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?

Consider anything *other than* a pure sine wave at x Hz.  Consider say a square
wave at x Hz, sampled at 2x Hz.  What do *you* envisage those sample will let
you reconstruct?

langwadt@ieee.org wrote:

    ..

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

Sometimes. If it's a closed-loop servo, maybe 5X oversampling is called 
for. I've written about why before. It's enough to say here that one 
sample delay is 180 degrees phase shift at the sampling frequency. 
Anti-alias filters have delays of their own. Sampling at 10 or 20 x can 
avoid the need for an anti-alias filter altogether. "It depends."

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

Genome wrote:

   ...

> I have noticed that for switch mode power supplies the loop crossover 
> frequency is Fs/2piD and have often modelled such things in spice and they 
> have behaved themselves where the loop crossover frequency is well above a 
> half of Fs which rather pisses on Nyquist....
> 
> What did I miss?

Spice models continuous systems. Isn't the iteration interval 
dynamically adjusted to be at least as small as needed?

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

rebel wrote:
> Consider anything *other than* a pure sine wave at x Hz.  Consider say a
> square  wave at x Hz, sampled at 2x Hz.  What do *you* envisage
> those sample will   let you reconstruct?

And the frequency of a square wave is what?
Hint, read up on Fourier series.

Sigh.
A square wave has infinite frequency, so what sample rate
do you propose?

All real signals are composites of sine waves in theory.
In practice, they usually don't have infinite numbers of composite
waves at infinite bandwidth.

BTW, a square wave can usually be expressed in four or six bytes.
just encode "squarewave, 10hz, 2 volt" and you are done.


-- 

On Tue, 22 Aug 2006 23:28:19 -0400, Pat Farrell <none@nospam.info> wrote:

>rebel wrote:
>> Consider anything *other than* a pure sine wave at x Hz.  Consider say a
>> square  wave at x Hz, sampled at 2x Hz.  What do *you* envisage
>> those sample will   let you reconstruct?
>
>And the frequency of a square wave is what?
>Hint, read up on Fourier series.

I'm fully aware of that, but thanks for passing the tip on for others.  That WAS
why I posed the question that way.

>Sigh.
>A square wave has infinite frequency, so what sample rate
>do you propose?
>
>All real signals are composites of sine waves in theory.
>In practice, they usually don't have infinite numbers of composite
>waves at infinite bandwidth.

Of course they don't, but the fourier series illustrates the point - the need to
sample at least twice per period of the highest frequency component present (in
a significant enough amplitude to matter wrt the sampling step)

>BTW, a square wave can usually be expressed in four or six bytes.
>just encode "squarewave, 10hz, 2 volt" and you are done.

For a sampling oscilloscope looking at an analog waveform, that isn't really
much help.

steve wrote:
> Tim Wescott wrote:
>
> > 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".
> >
> looks ok to me

Does it?

>and Mr Nyquist, I suspect,

No.

> ...what do you think the
> relationships should be

The answers are

a) Sample at Fs > 2X Hz
b) Cut-off at Fc < X/2 Hz

Note no equality signs here.

The sampling theorem states a *lower*bound* on the relation
between sampling frequency and the highest significant frequency
component in the signal.

There is nothing in the sampling theorem to suggest that
sampling at 2X Hz is *sufficient*.

Tiny detail in phrasing; huge difference in practice.

Rune

Tim Wescott wrote:
> 
> 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.

Just tell them that they've got to make sure that they sample BELOW the 
Nyquist frequency of the HIGHEST frequency present in the signal, and 
that the cutoff frequency of a filter isn't the frequency at which the 
output is effectively disappeared.

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.
> 
   How about a few observable facts.
   Like a signal at frequency F1 can be sampled at a rate F2 and the net 
is the phase difference if these frequencies are *exactly* the same, or 
if the ratio is exactly 1:2 or 2:1 or any other integer ratio.
   If there is a slight difference in the ratio F1/F2 or F2/F1, that the 
difference frequency is observable but no clue as to which one is the 
least stable with short term measurements.