Nyquist Didn't Say That

Andor: If your really interested you might look into the Muntz Polynomial theorems. They provide a way to approximate L2 waveforms. Resolving the equations would allow an almost arbitrary exponential basis, with the coefficients determined by sampled points. I also have some papers on irregular sampling around if your interested. My goal was determining "sampling" points for spectral analysis of IR absorbtions so it doesn't actually match up with this discussion smoothly. Sorry for the side issue, but I really think the Muntz theorems are neat and underutilized.

Ray

OK lets try it slowly now..... W h o ' s o n f i r s t ?

----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----

----= East and West-Coast Server Farms - Total Privacy via Encryption =----

You've lost me. But as you haven't put forward any alternate postign standard to debate, I can only conclude you aren't at all interested in logical discussion of the subject... which I must say figures, that you can't logically defend your standing.

Tim

... snip ...

You are basically describing the action of a sampling oscilloscope. This is not sampling at Fs/2, because the change in phase affects the sampling frequency.

I hadn't bothered with logical debate because you had already dismissed arguing against top-posting as irrational. That instantly moved you from 'candidate for logical discussions' to 'complete f****ng moron'.

Tim

I guess you're right if you read "measurable/objectionable" as "measurable _and_ objectionable". I read it as "measurable _or_ objectionable" without thinking to find a benefit of doubt.

Jerry

How would a phase locked loop lock without any additional samples (or equivalent information or measurements) prior to or during the exactly spaced Fs sampling? How would you know a PLL was in lock with no data other than fixed frequency samples? (even a "lock" signal would constitute one more sample, thus raising your sample rate to Fs+1)

IMHO. YMMV.

Unless you're willing to extend the meaning of 'Transfer Function' to be something like Y = H(s, X) instead of Y(s) = H(s) X(s), then no, strictly speaking, you can't. Are you indeed doing this?

You _can_ often make approximations that are more than good enough for many applications, however.

I'll agree with you, but only if you'll agree that that's a nit.

If you don't hook the detector and loop up to the input signal than it won't lock. If you do hook it up, then that is equivalent to taking at least one more sample (to do a phase comparison or something). So your sample rate is now greater than Fs by whatever measurements the detector made in order to convince you that the PLL is locked.

Of if you just looked at the output of the PLL, you would need a lock flag to know whether or not the PLL was locked or not. The lock flag constitutes at least one bit of information which increases the sample rate to Fs + 1 bit > Fs

If you don't look at the lock flag, the you won't have any idea what phase the samples were taken at. It could have been a DC level that the PLL couldn't lock to.

IMHO. YMMV.

Makes sense.

The practical consideration is that sometimes the anti-aliasing filter is chosen prior to knowing what might be connected downstream. For example, if some customer comes along wanting to hook up their 10 samples/sec receiver to the output, then they are probably going to be unhappy with the result.

Sometimes it happens in legacy systems where the ADC stage was built for a certain use, and later on other customers want to hook their receivers up to it. For everything to work best you'd need to modify all fielded units.

If I understand you correctly, the downstream system would need to receive ALL samples, then interpolate them for use at the slower 50 sample/sec rate. So in effect they'd still have to act on the data (interpolate) at the faster original rate. This makes sense to me, but the customer may balk at this. There's no ideal solution to this problem.

This discussion clarifies some things for me... thanks to all repliers.

...

The high-rate signal must be filtered and decimated before it can become low rate. Those process can be performed by what you call the up-stream system, by the down-stream system, or split between them. Although there may be modules, there is only one signal-flow path. What is non-ideal?

Jerry

No, you are the one that started the name calling and ad hominem attacks. To repeat Tim Williams question, "What Usenet news reader starts at the bottom of each post?"

In message , dated Sat,

I don't exactly start at the bottom, because I want to scan the quoted text to see what the current state of 'play' is. But I scroll down quickly, and if I find no new stuff, I utter a suitable expletive and go back to the top to see if anything is top-posted.

Thanks for the tip, Ray. Googling quickly revealed a paper titled "The Full M=FCntz Theorem in Lp[0,1] for 0 < p < inf" by Erd=E9lyi and Johnson. This is the first time I've heard about the M=FCntz theorem - very interesting! It might indeed pose the basis for approximating peridodic signals in Lp norm.

What else can you say about irregular sampling?

Regards, Andor

No? No what?

You know full well. What book starts with the epilogue?

Tim

I do not claim to have tried all the usenet news readers out there, probably not even half of the reasonably popular ones. I have etched into my brain to be very careful about making sweeping generalizations with insufficient data.

Do you know enough about all the usenet news readers to generalize so broadly?

(snip)

There is a story that L'Hopital's rule was formulated by Bernoulli, but L'Hopital bought all Bernoulli's ideas for some period of time, including that one.

So there is another way to get your name on a rule or law.

Fermi seems to have done pretty well, though. An element Fermium, distance unit (also called the femtometer, conveniently with the same abbreviation), Fermi energy, Fermi momentum, Fermi velocity, and probably more that I can't think of right now.

-- glen