# Nyquist Didn't Say That

Started by August 22, 2006
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?

Regards

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. > > -- > > 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
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?

Regards

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. > > -- > > 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
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?

Regards

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. > > -- > > 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
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?

Regards

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. > > -- > > 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
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 ' >'. -- Stef (remove caps, dashes and .invalid from e-mail address to reply by mail)
Tim Wescott wrote:
> 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. >
Does Wikipedia have a posting mode that allow only original author or a "approved" contributor to modify an article. I heard a recent story of how the Wikipedia article about an Arkansas city had derogatory comments inserted. Might the best approach be using "External links"? Tim keeps control. The "world" gets the information. If Tim gets paid for the article, the publisher gets site exposure.
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 ' >'.
Well, if you can guarantee that the cos has no phase shift, then you may have a cos term at Nyquist frequency in discrete periodic sequences without introducing aliasing ambiguity. OTH, any periodic, discrete sequence with Nyquist frequency will be interepreted as a cos (zero phase shift) by the discrete Fourier sum (aka DFT). For example, the sequence ..., 1, -1, 1, -1, ... will be interpreted as a cos with amplitude 1 by any (finite) DFT. The sequence ..., 1/sqrt(2), -1/sqrt(2), 1/sqrt(2), ... will be interpreted as a cos with amplitude 1/sqrt(2) as opposed to a unit amplitude cos with pi/4 phase shift. By defintion, the imaginary part of the Nyquist DFT coefficient is always zero for real sequences (just as for the DC coefficient, but we don't want to discuss phase shifts for DC signals again :-). Regards, Andor

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?
In theory you get nothing. In practice you get a good indication of just how non-linear and inaccurate your signal and sampling system really are. -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----
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. > > -- > > 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
More quantitatively, the various questions about anti-alias and sampling can be answered by reconstructing the signal from the proposed signal system and them computing the error for antcipated input signals by taking the difference (in simple systems). Put another way, model the signal processing path and compare it to what you want, to see if the approximations you make in your implementation matter. This provides guidance for sampling rates and anti-aliasing; vesus various input spectra/signals. In signal processing we typically approximate perfection (which is sometimes impossible) by various means; the adequacy depends upon the errors that we allow. Given a description of what we want and a proposed implementation the errors should be calculable. Nyquist moerely talks about what can be made to wrk given perfect resources; reconstruction of an incoming signal of a certain type. If you feed >2X signals or don't reconstruct/use the data optimally, you have to do the error analysis to see how much you are paying for not being perfect. In other words, you allways have to do an error calculation for an proposed design and enviroment. Ray Ray
sample and hold circuit needs sample interval more than twice frequency
of sample, but lower frequency sampling can be done if more than two
samplings is happening.

eg 1024Hz and 125HzHz => max freq descrimination = 2^10*5^3 Hz

cheers