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

# Nyquist Didn't Say That

Started by ●August 22, 2006

Reply by ●August 23, 20062006-08-23

Reply by ●August 23, 20062006-08-23

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

Reply by ●August 23, 20062006-08-23

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

Reply by ●August 23, 20062006-08-23

Reply by ●August 23, 20062006-08-23

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)

Reply by ●August 23, 20062006-08-23

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.

Reply by ●August 23, 20062006-08-23

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

Reply by ●August 23, 20062006-08-23

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 =----

Reply by ●August 23, 20062006-08-23

Tim Wescott wrote:

Reply by ●August 23, 20062006-08-23

Rune Allnor wrote:> 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. >Well yes, but that is only due to the fact if you sample at exactly 2x you might sample at the zero points of the the sin wave, and not be able to reproduce the signal, but most people write =2x because of convenience, but if 2.0000000000001 is how you like to write it, then ok.> 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