mobi wrote:> Another issue, > Isnt it important to always keep into mind what the recustruction > filter is? > > Lets consider this situation. > I have an output signal from a ZOH. I want to sample it again and > reconstruct it back. Now i think i need only one sample per ZOH symbol. > Why? Cos my reconstruction filter can construct my signal exactly from > one sample. Certainly i am not satisfying Nyquist in this case. Or > maybe i have not been sleeping to well :o) > > > Jerry Avins wrote: >> Jonathan Kirwan wrote: >> >>> ... You need some margin for the skirts, don't you? >> If course, and for other things too. Even if you can be certain that >> there is no signal energy above Fmax, you need to sample faster than >> 2Fmax in real situations. As it says on traffic a summons in Boston, >> "Fail ye not thereof at your peril."_______________________________________________________________________ Engineering is the art of making what you want from things you can get. -- Jerry Oh, yes: please don't top post. It makes sequence hard to follow. implications of the sampling theorem needs broadening. pair, or, as in your example, magnitude and derivative. Your view of the cycle. They can be individual samples, they can be a real/quadrature The sampling theorem requires at least two pieces of information per that the derivative is zero at the instant that the sample is taken. case, that its derivative is zero /almost everywhere/. In particular, You are taking advantage of additional knowledge of the signal; in this
Nyquist Didn't Say That
Started by ●August 22, 2006
Reply by ●August 24, 20062006-08-24
Reply by ●August 24, 20062006-08-24
Steve Underwood wrote:> Rick Lyons wrote: > [...] >> Hey Tim, >> I think in any dissertation on "sampling" it would be a good idea to >> discuss bandpass sampling. >> Bandpass sampling is not only an interesting topic, but it's a very >> practical topic in these days of digital communications. (Just my two >> cents.) > > And complex sampling. You must include that, otherwise people won't > understand the solid unshakeable reality of negative frequencies. :-)That again? I can show you the trig that explicates "complex" sampling without resort to negative frequencies, but so what? :-) I think a generalization needs to be hammered home. *Any* two independent measurements will do. Value and derivative, for example, as I mentioned by way of explaining why only one sample per cycle is needed to reconstruct the output of a zero-order hold. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 24, 20062006-08-24
Rick Lyons wrote:> On Tue, 22 Aug 2006 15:23:14 -0700, Tim Wescott <tim@seemywebsite.com> > wrote: >-- snip --> > Hey Tim, > I think in any dissertation on "sampling" it > would be a good idea to discuss bandpass sampling. > Bandpass sampling is not only an interesting topic, > but it's a very > practical topic in these days of digital > communications. (Just my two cents.) > > See Ya', > [-Rick-] >Enough people have mentioned this that I'm going to have to give it serious consideration, but I think I may just point out the existence of bandpass sampling (and complex sampling) then write a follow-on article. I certainly agree with your statement about the sampling process being so often misunderstood. I think this is because sampling seems so simple, yet there is a ton of unintuitive results flowing just below the surface. -- 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 24, 20062006-08-24
Thad Smith wrote:>> 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. > > > I'm not an expert in this area, so maybe you can clarify something.If the signal constellation has N different phases, then you will have to multiply the phase error by N in order to suppress the influence of the data. The simplest example of that is the squaring Costas loop for BPSK. Any kind of non data-aided PLL will have to do this multiplication of phase. It is typical for modems that the carrier PLL operates once when the current symbol is strobed. Thus if the carrier offset is higher then +/- Baudrate/(2*N), the PLL will not lock properly.> If the carrier > frequency is fixed, I would expect that the bandwidth of the PLL would > be narrow enough to exclude the aliased frequencies.It is not always possible, especially if the carrier is RF and if the incoming SNR is low. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●August 24, 20062006-08-24
Jerry Avins wrote:> > Of course you can lock the sampler to the sampled waveform or one of its > harmonics. Google for "PLL". >I can google PLL, but I wasn't aware that this extra timing circuitry that you are belatedly introducing to the discussion was included in the theory being discussed. Just exactly how does it fit? You already have a switch on the microphone you could just switch it off if you are going to resort to introducing a phony solution - why would you need to go to all the trouble of a PLL? -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 24, 20062006-08-24
jim wrote:> > Jerry Avins wrote: > >> Of course you can lock the sampler to the sampled waveform or one of its >> harmonics. Google for "PLL". >> > > I can google PLL, but I wasn't aware that this extra timing circuitry > that you are belatedly introducing to the discussion was included in the > theory being discussed. Just exactly how does it fit? You already have a > switch on the microphone you could just switch it off if you are going > to resort to introducing a phony solution - why would you need to go to > all the trouble of a PLL?You introduced what you claimed was a practical difficulty of phase lock in the real world into a theoretical discussion about sampling at a fixed phase offset. I pointed out one practical way to overcome the perceived difficulty. If you knew it all along, what was your cavil about? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 24, 20062006-08-24
Jerry Avins wrote:> > Of course you can lock the sampler to the sampled waveform or one of its > harmonics. Google for "PLL".Not all signals are periodic waveforms.
Reply by ●August 24, 20062006-08-24
Jerry Avins wrote:> > You introduced what you claimed was a practical difficulty of phase lock > in the real world into a theoretical discussion about sampling at a > fixed phase offset. I pointed out one practical way to overcome the > perceived difficulty. If you knew it all along, what was your cavil about?I didn't introduce anything. A question of fact was asked "What would happen?" - someone else responded incorrectly - I responded to that response. You snipped all that and now accuse me of introducing the question. If you are going to trigger the sample timing to twice the highest frequency component, then you should have no trouble measuring the amplitude of that frequency component. So apparently you are now saying that those who say you need to sample at more than twice the rate are completely wrong, since there is a practical way to overcome the perceived difficulty. -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 24, 20062006-08-24
"Richard Henry" <pomerado@hotmail.com> wrote in message news:1156426475.306460.133630@75g2000cwc.googlegroups.com...> It has been my experience with local engineers' groups that the people > who get awards are the ones who show up regularly.My mother took a gym class once (this would have been in the early '60s) where something like 20% of the exam score was for putting your name on the paper... she purposely chose to not do as a form of protest. :-) Where I used to work, rumor had it that the main reason a trade rag had just given our device a "widget of the year" award was due to marketing commiting to a high dollar advertising campaign with said trade rag. Hmm... (Those of us in engineering who knew how, uh... lackluster... the widget's performance was knew it could have never won on its technical merits.)
Reply by ●August 24, 20062006-08-24
jim wrote:> > Jerry Avins wrote: > >> You introduced what you claimed was a practical difficulty of phase lock >> in the real world into a theoretical discussion about sampling at a >> fixed phase offset. I pointed out one practical way to overcome the >> perceived difficulty. If you knew it all along, what was your cavil about? > > I didn't introduce anything. A question of fact was asked "What would > happen?" - someone else responded incorrectly - I responded to that > response. You snipped all that and now accuse me of introducing the > question.I apparently misunderstood the thrust of your message, quoted in full here: <begin quote> Robert Baer wrote: > > > > 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? Aint i statisifying >> > > Nyquist here? >> > > > > >> > > > > Yup! > > Also try sampling at a constant delay from the sine zero crossing. > > That is what happens when people blindly follow a "criteria" without > > knowing the full reason and background. What is what happens? Do you actually know what happens if you actually try this in a real world context? Set up a speaker generating the Fs/2 signal. Set up a microphone and and ADC to record the sound at Fs. Are you claiming that you can adjust the sampling phase to produce a digital recording of either full scale or zero? That's what in theory should happen - right? But can you do that in real life? -jim <end quote> If you derive the speaker excitation from the ADC clock, there is no difficulty maintaining whatever phase relation you decide upon. What did I not understand? What was the incorrect response you addressed?> If you are going to trigger the sample timing to twice the highest > frequency component, then you should have no trouble measuring the > amplitude of that frequency component. So apparently you are now saying > that those who say you need to sample at more than twice the rate are > completely wrong, since there is a practical way to overcome the > perceived difficulty.I don't get it. What have I written that makes it seem that I believe the amplitude of a component f can be determined by sampling at 2f? We both know it can't be done, and why. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
