# Nyquist Didn't Say That

Started by August 22, 2006
```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
http://www.wescottdesign.com

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

So, if you need to monitor a signal that occurs at xHz - what frequency
should you sample it at?

D
```
```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 and Mr Nyquist, I suspect, ...what do you think the
relationships should be

```
```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,
or
b) in baseband sampling, the notion that in practice, one needs to
sample faster than 2X Hz to measure something at X Hz?

(or both)?

--
Oli
```
```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

```
```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 and Mr Nyquist, I suspect, ...what do you think the
> relationships should be

I'd guess he wants the word "periodic" in there somewhere (:

```
```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.

--

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

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

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...

--

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

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
```
```"Tim Wescott" <tim@seemywebsite.com> wrote in message
news:q6mdnZgxjJhQHnbZnZ2dnUVZ_rGdnZ2d@web-ster.com...
> 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
> http://www.wescottdesign.com
>

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?

DNA

```
```Tim,
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?

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