Tim Wescott wrote:>... snip ...> > Actually designing for the sin x / x rolloff isn't too bad as long as > you keep your eyes open -- in older digital video systems it was just > done with a peaky 2nd-order LC circuit (in newer digital video systems > the sampling rate is way higher than the effective resolution of the > phosphor, which simplifies things). > > But you can't avoid the issue of providing sufficiently steep skirts on > your filters, both in and out. As you get closer and closer to Nyquist > in a 'simple' system your filter complexity goes through the roof, as > does the difficulty of actually realizing the filters in analog > hardware. This is why many systems that must store or transmit data at > close to Nyquist (like music on a CD) have A/D and D/A sample rates that > are significantly higher than the internal transmission rate, with > digital decimation and interpolation coupled with simplified analog > anti-alias and reconstruction filters.IIRC the sin x / x business only applies to sample and hold filtering. The impulse function avoids that. A further point is that the thing that counts in an end to end system, such as telephony, is the net transfer function. You can distribute this in various way with compensating input and output filters. This is generally known as equalization. -- Chuck F (cbfalconer@yahoo.com) (cbfalconer@maineline.net) Available for consulting/temporary embedded and systems. <http://cbfalconer.home.att.net> USE maineline address!

# Nyquist Didn't Say That

Started by ●August 22, 2006

Reply by ●August 23, 20062006-08-23

Reply by ●August 24, 20062006-08-24

Somewhere in the Nyquist discussion, you might mention that Nyquist didn't attend MIT or Stafford. He went to a small obscure school in North Dakota. Robert, Did I miss anything? -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com

Reply by ●August 24, 20062006-08-24

FOAD. It was a short, to-the-point comment. The only possible rational argument that can be made to his post is that he didn't trim the quoted text. Tim -- Deep Fryer: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms "CBFalconer" <cbfalconer@yahoo.com> wrote in message news:44EBA509.124CD03F@yahoo.com...> *** top posting fixed *** >> 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? > > Don't top-post. It is rude and contravenes the standard practices > in newsgroups. Your response belongs below, or intermixed with, > the *snipped* material you quote. See the links in my sig. below.

Reply by ●August 24, 20062006-08-24

"Jim Stewart" <jstewart@jkmicro.com> wrote in message news:UaidnVPZ369OFXbZnZ2dnUVZ_t-dnZ2d@omsoft.com...> I'd guess he wants the word "periodic" in there somewhere (:HIO4? Tim -- Deep Fryer: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms

Reply by ●August 24, 20062006-08-24

Scott Seidman wrote:> > CommitteeSize = CommitteeSize + 1 ; %!!!!! > > I think what's missing is a demonstration that multiplication with the > Dirac train in time pairs with convolution with the scaled Dirac in > frequency. Without a good figure showing that, the figures under the > "aliasing" subtitle lack some meaning.well, then maybe they should be moved the the "mathematical basis", then. you don't need the convolution with the Dirac comb in the frequency domain thingie if you can show by some other means (i think simpler means) that the spectrum is copied and shifted at all multiples of the sampling frequency. we can show that by showing that the Dirac comb is a periodic function with identical coefficients (all 1 if you scale it right) and then using the frequency shifting theorem.> > As an aside, I'm interested in the analogs in AM. By the book, the > carrier needs to be twice as fast as the highest signal component, but > for Hilbert demodulation, all I can find is the specification that the > signal and carrier not overlap. Is this because the transform > essentially throws out the negative frequencies, so you don't have to > worry about positive/negative overlap?i think so. this kind of AM modulation is called SSB. at least that's what we called it when i was a ham radio kid 38 years ago.> Alternatively, am I just wrong, > and the carrier needs to be twice the highest frequency, even for Hilbert > demod??duh, i dunno. i think, if you do it the Hilbert way (we didn't have DSP in them olden days of the Heathkit HW100) you can have a carrier frequency of whatever you want. you can separate the positive and negative parts of the original baseband signal and move the positive up or down any amount with the negative part doing the mirror image and moving down or up the opposite amount. r b-j

Reply by ●August 24, 20062006-08-24

On 23 Aug 2006 10:39:59 -0700, "steve" <bungalow_steve@yahoo.com> wrote:>Jerry Avins wrote: >> steve wrote: > >> No; it's more than that. It means (among other problems) that there's no >> way to determine the component in phase with the sample clock (sine >> component), so the amplitude remains unknown. >> >sampling at 2.000001X solves that problem, there are no frequencies in >phase with the sample clock anymore, the point I was making > >There is no additional information obtained by sampling at a higher >rate.True, but the "information" on a periodic waveform will be all garnered one helluva lot quicker at 2.1x than at 2.000000001x

Reply by ●August 24, 20062006-08-24

CBFalconer wrote:> Tim Wescott wrote: > > ... snip ... > >>Actually designing for the sin x / x rolloff isn't too bad as long as >>you keep your eyes open -- in older digital video systems it was just >>done with a peaky 2nd-order LC circuit (in newer digital video systems >>the sampling rate is way higher than the effective resolution of the >>phosphor, which simplifies things). >> >>But you can't avoid the issue of providing sufficiently steep skirts on >>your filters, both in and out. As you get closer and closer to Nyquist >>in a 'simple' system your filter complexity goes through the roof, as >>does the difficulty of actually realizing the filters in analog >>hardware. This is why many systems that must store or transmit data at >>close to Nyquist (like music on a CD) have A/D and D/A sample rates that >>are significantly higher than the internal transmission rate, with >>digital decimation and interpolation coupled with simplified analog >>anti-alias and reconstruction filters. > > > IIRC the sin x / x business only applies to sample and hold > filtering. The impulse function avoids that. A further point is > that the thing that counts in an end to end system, such as > telephony, is the net transfer function. You can distribute this > in various way with compensating input and output filters. This is > generally known as equalization. >It applies in spades to zero-order holds on the output, AKA garden-variety DACs. And where aliasing is a problem, there's more to it than the end-to-end transfer function -- strictly speaking you can't formulate a laplace-domain transfer function for a time-varying system, such as a system that incorporates sampled data. -- 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

Tim Wescott wrote:> steve wrote: >[...]> >> Nyquist assumes the ideals, you can't have a theorem otherwise. >> > That's true. The problem comes about when newbies who have forgotten > all of the addenda, exceptions and quid-pro-quos* assume that Nyquist is > a design guideline instead of a theoretical limit.The sampling rate is an entirely practical limit in systems which embrace the aliases, rather than trying to eliminate them. In those cases the "practical limit" is not the sampling rate aspect of the sampling theorem, but how well you can approximate the ideal sampler. Steve

Reply by ●August 24, 20062006-08-24

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? > > 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 > >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.

Reply by ●August 24, 20062006-08-24

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 ' >'. > >...then re-state with sampling at 2X+delta where delta is (say) 1Hz!