Nyquist Didn't Say That

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?

News==----

Newsgroups

I suggest that you draw the waveforms, selscting some arbitrary but fixed phase relation, then re-draw with a slightly different phase relation.

They'll never notice (unless they read this group). Their local boy has been published and has therefore made good, so he gets the award.

As I remember it, Nyquist wasn't sampling at all. He was trying to get telegraph pulses through a cable, and wanted to know how close together the pulses could be.

Instead of sampling a continuous signal, he wants to send a sampled signal (pulses) though a band limited channel.

It happens to be the same math, and so he gets the sampling theorem, also.

-- glen

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I don't think you participated, Rick, but I while ago I posted a DSP riddle about regular sampling of periodic and continuous signals with known period (here:

Under those conditions I showed that it is possible to arbitrarily well approximate the periodic signal from the regular samples, given enough time. Further, I showed that this is possible even if the signal is a) not bandlimited, and/or b) the sampling frequency was bounded by some given value (ie. undersampling).

The proposed reconstruction process does not involve sinc interpolation, but rather synthesis with truncated Fourier sums. I thought it was rather neat, but reactions here ranged from disbelief to stating that this was trivial. I haven't worked it out yet, but I think the scheme is extendable to the case where the period of the signal is unknown (using two regular samplers with irrational sampling periods).

Regards, Andor

Does that also work if he is published in the National Inquirer? :-)

Steve

Agree. Bessel unfortunately can't be used for high slopes. But with a custom design even the Chebashev can be made to keep the time delay into reasonable limits as long is used far enough from Nyquist limit (in frequency domain). I've seen solutions using FIR filters (24 to 32tap at 16Mhz sampling), but some dirt can't be rejected and still need and auxiliary analogic filter. Not talking about DSP or processor time required by such filter...

Vasile

Of course, I've thinking to Cauer, sorry.

Vasile

Of course you can reconstruct some signals with slow sampling - it is done all the time in sampling oscilloscopes. This requires a trigger related to the repetitive signal and a moving time delay. But this is not a real-time operation, as is the usual sampled reconstruction of a complete waveform.

(snipped)

Hi R B-J, The Smith article (and all the Letters to the Editor) are probably somewhere on the IEEE website. That's only useful to you if you've won the lottery and can afford to subscribe to the IEEE's XPlore program.

The first Fonte article is not online, as far as I can tell. For people who subscribe to the Circuit Cellar magazine, I'll bet that the

The Bonnie baker article is at:

See Ya', [-Rick-]

Hi, you may be right about that. I once read something on the Internet written by a guy who was having lunch (one afternoon at a university cafeteria) with Claude Shannon. The writer said that Shannon stated that it he (Shannon) who named the sampling theorem after Nyquist.

See Ya', [-Rick-]

(snipped)

Hi, How would I go about reading about (1) "this guy", and (2) what he's written about the topic of sampling?

Thanks, [-Rick-]

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It's amazing how quickly technology goes from magic to mundane. As you say, negative feedback was magic in the 20s. It wasn't widely used in audio until the late 40s, when new post-war designs began to be produced, and then only in "audiophile" equipment. The console radio-phonographs sold immediately after VJ Day and at least through

By the early 50s, with no formal training, I was reworking the guts of Capeharts and Magnavoxes to cut distortion from about 8% at 6 watts to less than 1% at 12 watts. I replaced the original speakers (salvaging their magnets for continues use as power-supply chokes), but otherwise reused the original parts. (Actually, I had some left over when I was done. I saved some of them. Does anyone want a radial-lead body-end-dot carbon resistor?) I lined the cabinets with felt and closed the backs. Usually, I replaced the 78 changer with a Garrard that also played LPs; then I needed to add a phono preamp: a single 12AY7.*

Was I in my late teens smarter than the engineers who designed the original circuits when I was not quite ten? No way. I had the benefit of the intensive developments of the war years, encapsulated in the back of the RCA tube manual, in the ARRL handbook, and in books like the MIT Radiation Lab's "Principles of Radar".

Jerry ___________________________________________

• The first conversion was for a family friend who generously allowed me to tinker with his Capehart. All the rest were paid projects for people who had heard the original or a later conversion. What began as tinkering led to a profession. "Now I are one."