Nyquist Didn't Say That

The Nyquist criterion tells you if your closed-loop feedback system will be stable or not. It has nothing to do with sampling.

-a

You're thinking of the Barkhausen criterion, which gives a necessary, but not sufficient, condition for oscillation. While it's useful for building oscillators, it doesn't help you tell if your control system is stable or not -- and having built plenty of type III control systems I can assure you that 180 degrees of phase shift and gain >> 1 doesn't mean you're oscillating.

The Nyquist rate is about sampling, and while I haven't heard it called a "criterion", it's still about sampling.

What really happens is that you get a signal at Fs/2 that is sometimes big and sometimes small, and you have no clue if it's _actually_ a signal at Fs/2 that's sometimes big and sometimes small, or a signal that's big and sometimes at Fs/2 and sometimes slightly off.

Which is a bad thing.

Which is why you don't want to do it.

The Nyquist sampling theorem. We weren't carrying on about enclosing the point -1, 0 on a Nyquist plot in the s plane. That guy Nyquist had more than one feather in his cap. Spirule, anyone?

Jerry

But see

Jerry

I wonder if he really means Chebyshev or elliptic (Cauer)? They both ring badly, but the Cauer rings like a bell if you design one for any reasonably steep cutoff slope. In a particular application you might not care directly about the ringing. However it badly compromises the anti-aliasing qualities of the filter, since it can allow bursts of out of band energy through.

Steve

Do you think it will change for the better or the worse? It seems numerous articles on Wikipedia start out pretty good, but editors much less knowledgeable than the original author gradually scramble them.

Why would that be? If people are paid to do a good job writing articles, they might possibly do so. Right now, any financial or other personal gain from contributing lies outside Wikipedia, leading to blatant agendas in the writing. I think giving prominence to the names of valued authors might be a solid incentive to good work.

Someone pointed me to the Wikipedia articles on a couple of p*rn stars. From there you can link to many others. They seem to have been written with a genuine affection and interest for the subject matter. I was amazed to see how much effort people will put into that. If they could only encourage a similar level of dedication in the technical articles Wikipedia could become outstanding. :-)

Steve

OK.

Maybe. There are situations where it doesn't matter if its a fluctuation in the amplitude or frequency. Like a 44khz sound recording where your ears can't discern the difference anyway. Bad or good always depends on what you are attempting to accomplish. I never said it was a good thing or a bad thing. What I did say was sampling a sine wave at Fs/2 mo matter what you think the phase is produces a good indication of how non-linear and inaccurate your signal and sampling system really are.

-jim

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No, not re-sampled (from analog to digital) by each system, but instead sent digitally to the next system such that the receiving system only uses some of the data, not every sample. Let's say the initial ADC step has a 1000 samples/sec conversion rate, then the signal is broadcast out, and a receiver system receives at a rate of 200 samples/sec. Then the processing inside that system only has time to perform 50 calculations/sec.

Would the analog anti-aliasing filter selection be dependent on the 50 calc/sec? If that's true you'd have to select the aliasing filter based on the slowest end user of the data. It seems odd that if you design an ADC stage, you'd have to choose analog filtering based on the slowest performing "weakest link" in the eventual design. Opinions?

It's not a matter of opinion; this is well charted territory. Look up interpolation and decimation, or up- and down converting. Digital filtering is usually required at each stage.

Jerry

well, you said this:

and you said this:

i didn't realize you were being facetious here.

...

we know what happens when you sample something at precisely Nyquist. it only matters what relative phase the sampling is done on and the rest is unremarkable. there is nothing else that happens.

r b-j

Not really, that's exactly what bottom posters would have.

Do you honestly like those posts that are 11KB in size, yet have one single line of original text at the very bottom?

That's beside the point, you're smart enough to see the quoting level. Oh wait..maybe you aren't.

Tim

Y'know, I use that all the time, but I totally forgot it's name.

Whadda ya know.

AFAIK Nyquist got his first fame with the analysis of negative feedback in vacuum tube amplifiers back in the '20s when it was all magic. _Then_ he got into cahoots with Shannon to make his rate.

When I said 'resampling' I meant precisely the step where you go from

In my opinion that would be a pretty odd system.

Without opinion, if you interpolate correctly before you decimate then no, you wouldn't have to take that end-use 50 sample/sec into account at the initial stage. If you don't, you do.

Just jumping in here for a second (and I'm not sure if this is being debated or not) but I thought the second part of Nyquist is, to reconstruct your samples you pass them through an ideal low-pass filter.

The ideal low-pass has the impulse response of sin(x)/x aka sinc(x) and as you pass your impulses through it, the filter "perfectly" interpolates the data between the input impulses. This works as long as you satisfy the sampling rate (whatever that is) and your low-pass has infinite roll-off.

Obviously real world re-construction filters do not have that...

John.

Correct.

Yes.

Correct. In fact, any filter that has a frequency response that goes to zero and stays there must have an impulse response that extends infinitely into both positive and negative time. This means that a real-world version of that filter will have to have infinite delay, which is kind of hard to implement (but easy to fake -- "Well boss, you said 'perfect' filtering, so we're just waiting for the response to be non-zero here. Don't hold your breath.").

How do you lock your sampling points to the signal with taking additional samples (or equivalent information or measurements)?

The scope trigger is, in fact, an additional measurement, thus giving you a total sample rate higher than Fs (as in total measurements per second) when the trigger is enabled. With the trigger off, how would you know if your sampling points were locked or not?

IMHO. YMMV.

... snip ...

Think about it. If you drop 4 out of 5 samples to get tothe 200 samp/sec, what is the difference (to the receiver) from original sampling at 200/sec. You have to consider the overall system.

...and when will their faces and the egg collide?