Nyquist Didn't Say That

I didn't introduce anything. A question of fact was asked "What would happen?" - someone else responded incorrectly - I responded to that response. You snipped all that and now accuse me of introducing the question.

If you are going to trigger the sample timing to twice the highest frequency component, then you should have no trouble measuring the amplitude of that frequency component. So apparently you are now saying that those who say you need to sample at more than twice the rate are completely wrong, since there is a practical way to overcome the perceived difficulty.

-jim

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My mother took a gym class once (this would have been in the early '60s) where something like 20% of the exam score was for putting your name on the paper... she purposely chose to not do as a form of protest. :-)

Where I used to work, rumor had it that the main reason a trade rag had just given our device a "widget of the year" award was due to marketing commiting to a high dollar advertising campaign with said trade rag. Hmm... (Those of us in engineering who knew how, uh... lackluster... the widget's performance was knew it could have never won on its technical merits.)

I apparently misunderstood the thrust of your message, quoted in full here:

Robert Baer wrote: > >

What is what happens? Do you actually know what happens if you actually try this in a real world context? Set up a speaker generating the Fs/2 signal. Set up a microphone and and ADC to record the sound at Fs. Are you claiming that you can adjust the sampling phase to produce a digital recording of either full scale or zero? That's what in theory should happen - right? But can you do that in real life?

-jim

If you derive the speaker excitation from the ADC clock, there is no difficulty maintaining whatever phase relation you decide upon. What did I not understand? What was the incorrect response you addressed?

I don't get it. What have I written that makes it seem that I believe the amplitude of a component f can be determined by sampling at 2f? We both know it can't be done, and why.

Jerry

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Engineering is the art of making what you want from things you can get.
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We are evidently dealing with a periodic waveform in a discussion of sampling at constant phase. Why drag in a non sequitur?

Jerry

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Rick Lyons wrote: ...

are any of these online?

Rick, i fear that similar stuff is being done in the Wikipedia article. this guy (whose name is very similar to yours and claims to have Alan Oppenheim and Ron Schafer as friends) would say to you that "the converse of the Nyquist-Shannon sampling theorem is not true", meaning that there are cases where frequency components at or above the Nyquist frequence can be validly reconstructed under some circumstances. i think he's talking about bandpass sampling.

Anyway, Wikipedia is so selective in the qualifications of editors, i am not sure how this experiment will turn out. sometimes very well written articles get "improved" by some editor that comes in who knows something about the topic (a little bit of knowledge is a dangerous thing) but makes edits that interrupt the flow of concept of the older version. there is no guarantee that the articles will improve in time. sometimes they get worse.

r b-j

It certainly can be done if your sampling points are locked to the signal. As usual your arguments consist of having you cake and eating it too.

-jim

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It can only be done if the sampling clock is known to be in quadrature with the second harmonic on the signal; the sampling occurs on the peaks. The cases discussed were about sampling at or near the zero crossings.

Prior knowledge of the sampling conditions and the signal can lead to systems of equations much simpler than the general cases that were under discussion. Knowing that the samples are taken at the peak od a sine of known frequency allows complete characterization of the signal with a single sample. I don't find such simplifications interesting.

Jerry

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Jerry Avenues wrote: Knowing that the samples are taken at the peak od a sine of

So why did you introduce it into the discussion in the first place?

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Because knowing the relative phase of the sampler to the signal's second harmonic is the only condition that makes possible the determination of amplitude when sampling at at 2f, a scenario that you introduced.

Jerry

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I don't know if he is talking about bandpass sampling. In fact, I have to admit that I'm not even sure of the exact definition of bandpass sampling.

However, consider wavelet transform and particularly signals produced by the wavelet synthesis. Such signals have theoretically infinite bandwidth assuming that the scaling function has finite support. This is true also when signals are synthesized only in truncated resolution (i.e. from scale u to v where u and v are finite). It's true even when synthesized in single resolution. Here synthesis means:

f(t) = sum_s sum_n x_s[n]*phi_n_s(t), where

phi_n_s(t) is the scaling function with translation n and scale s and x_s[n] are the samples from scale (or resolution) s.

Even though these signals have infinite bandwidth, they can be sampled and when given the correct scaling function these samples correspond to the original samples used in wavelet synthesis. Here sampling means

x_s[n] = ,

where f is the analyzed (sampled) function, phi is the scaling function with translation n and scale s. It is obvious that the signal can be later perfectly reconstructed from the samples by wavelet synthesis (assuming the scaling function matched the scaling function used in the original synthesis).

In fact, sinc function is just one possible scaling function (in which case one talks about shannon wavelets). This makes traditional sampling just a special case of wavelet transform (in single resolution). Note that the previous comment about infinite bandwidth does not obviously apply to shannon wavelets.

Any comments, or corrections?

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Jani Huhtanen
Tampere University of Technology, Pori

In message , dated Wed, 23 Aug 2006, Tim Williams writes

Yes, unionised.

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I'm not entirely agree with that. There are a lot of analog antialising filters, which are quite good near the Nyquist. One of them frequently used is the Cebashev filter (eliptical filter) which design and implementation is easy up to quite high frequencies (say 100-200Mhz, at least tested by myself).

greetings, Vasile

works really good when the sampling points are locked to the zero-crossings of the Nyquist frequency signal.

(snicker)

sounds to me that expecting a sampler to be phase locked to what we would normally think is an unknown signal (if it were known, why bother to sample it to determine its amplitude?) is having one's cake and eating it too.

r b-j

Ah, always nice to see people take the ad hominem route out. Fallacious though.

So tell me, how is it more convienient to anyone that a message be at the bottom of more than 30 lines of quoted text?

I'm not familiar with any newsreader which starts viewing at the bottom of a post.

...Hmm this was crossposted a lot. That's better...

Tim

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Ah, always nice to see people take the straw man way out. Fallacious though.

I'm not familiar with any other medium in the English language in which the reading order is bottom to top.

Tim

In message , dated Thu, 24 Aug 2006, Tim Williams writes

It isn't, unless it's a convention of the NG that that's where you look for new text.

Like with many things, there are advantages and disadvantages of bottom-posting, but it's what we do on this NG.

Of course, it's often quite unnecessary to quote 30 lines of text.

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John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK

... snip ...

That's fine if you don't care about phase linearity (time delay). Chebychev filters are notoriously poor at preserving phase, or having constant delay characteristics. This results in heavy distortion of analog waveforms, and will manifest itself as such effects as overshoot and ringing. A Bessel filter is designed to minimize this effect, but has much more gentle rejection slopes.

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Is there an echo in here. The above is exactly what I just said.

The question was asked - What really happens when you sample a frequency at Fs/2.

Set up a speaker generating the Fs/2 signal. Set up a microphone and ADC to sample the sound at Fs. What really happens? If you adjust the phase of the sampling can you record silence? This was not a theoretical question. We all know how it should work in a perfect world. How does it work in the real world?

No locking the ADC to the signal allowed since that would be a completely different question that no one asked and no one is interested in.

-jim

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However the phase information fed to the PLL to allow it to lock would constitute additional samples, thus raising the total sample rate of all information coming into the system above Fs/2. You have to count all the samples, not just the ones you label as "samples".

IMHO. YMMV.

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