Nyquist Didn't Say That

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

No, I do not like your straw man. But well done building him, he's very impressive. Almost as good as the picture of a cat made of dried pasta you made last week.

Tim

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."

I would disagree with that; you can formulate it. Using it is difficult except numerically; in my experience. Most any time varying function (including time varying coefficients) has a Laplace and Fourier transform. In the case of finite apature S/H or autozero systems you have to make up fancy equivalent circuits (time domain analogs of thevin equivalent circuits) and then write in transform equivalences. In the case of random noise or signals you have to resort to the power domain S(s)*S*(s) . Althought there is a systematic method for dealing with impulses of any order and position; I have never found a systematic way of creating the above equivalent circuits; for finite apatures and autozero circuit inclusion.

Ray

Tim,

I hope you'll be very careful with the "interesting" part. Too often I see it referred to as "frequency of interest" - which is very misleading. I think "interesting" means "has enough energy to have measurable aliases" and "of interest" may mean, to some, "the only part of the signal that I care about" to the exclusion of higher frequency components of significant energy.

This thread is so long that I can't really tell if anyone touched on this.....

For others: one must sample at a frequency that is greater than 2X the highest frequency *content* - where "content" is a subjective term indicating there is significant enough energy to cause measurable/objectionable aliasing.

Fred

Fred

i think all of this is correct.

he doesn't get the theorem exclusively (Shannon's name gets attached), but he gets the "Nyquist frequency". wouldn't it be t*ts to have the "Herrmannsfeldt impedance" ubiquitous in the lit?

r b-j

In article , Tim Wescott wrote: [....]

That is not true, if you allow a filter to have an infinit delay. It is only if you ever want to see the middle of the output that you have to have a response extending before the input.

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This is an awfully complex subject, with ramifications that are easy to overlook. Even the last statement, "... *content* is a subjective term indicating there is significant enough energy to cause measurable/objectionable aliasing" needs qualifying. To be strict, one needs to add "measurable/objectionable aliasing *into the band of real interest*". Other aliases can be filtered out. Accurate and definitive statements not subject to nit picking are exceedingly hard to make (at least without Wescott's tortured syntax). :-) That's why it's an art.

Jerry

Jerry,

If it wasn't "into the band of real interest" then it wouldn't be measurable/objectionable. To say more seems like "quantifying" rather than "qualifying" - e.g. "this band vs. that band, etc."

I don't know that math and hard work are really artful. One does need to know what one is doing. Knowing what is too big to ignore is calculable most of the time.

Fred

Phase locked loop. Communication systems do it all the time.

Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.