Impossible sampling theory!

A number of texts suggest that sampling can be modelled
by multiplying the incoming waveform by a comb of
Diracian Delta Functions.
How can this be?
1. The samples that you get are measured in the order
of single volts whereas the Diracian is infinitely tall. Surely,
if something of the order of unity were to be multiplied by
something of the order of infinity, the result would
be of the order of infinity?
How do you account for the difference? Do you have
some internal mental model where there is an invisible constant,
"Big K", perhaps, to account for the difference in scaling?
2. The area of the sampled pulse is very much less than unity,
the volts being ooo unity and the time being typically ooo usecs.
How do you handle this mentally when the area of the Diracian
is unity?
How do you come to terms with the attributes of your claimed model
being orders of magnitude different from the signals of the real world?
3. If you are one of those who claim that the sampled signal is a short
spike of zero width, then it is zero-integrable and not analysable by
any process involving Laplace Transforms.
How do you overcome the problem that your sampled signals are
not representable in the way that you claim?
Reply to
Airy R. Bean
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Huh. A second ago you denied ever saying that every text on the planet is wrong. Can you name a _relevant_ text, that being a text that discusses this issue, that denies what you just said?
No, it's not infinitely tall. It's not a function.
But it's true that after you do that sampling what's left is no longer a function (at least not a function defined on R).
How do you account for the fact that you ask us all these silly questions, even though you're determined to pay no attention if anyone tries to explain?
************************
David C. Ullrich
Reply to
David C. Ullrich
And I haven't said it below. Are you a troll?
And what I denied ever saying was that every textBOOK was wrong.
You'ew changing your goalposts by the minute.
Reply to
Airy R. Bean
Why would there be any texts that deny that "A number of texts suggest that sampling can be modelled by multiplying the incoming waveform by a comb of Diracian Delta Functions"?
What texts do you suggest would discuss other texts in that manner?
Reply to
Airy R. Bean
How tall do you think it is for the multiplication to take effect in a real circuit?
Reply to
Airy R. Bean
One of my professors implied that the Dirac delta wasn't mathematically rigorous but provides correct results so it's used nonetheless.
Reply to
Kevin Neilson
how old are you beanie?
you cause a lot of problems. thats my observation
interesting indeed. whats in it for you? do you learn from this group? do you provide input that others appreciate?
dr. x
Reply to
James Bond
It can be mathematically rigorous if you were to use the curve borrowed from the Normal Distribution of statistics, but it cannot produce the correct results for the simple reason that the pulses obtained are several orders of magnitude different from the pulses in real circuits.
(And if you regard the pulses produced in real circuits as existing only at a point, then those pulses are not analysable)
In all aspects of engineering, the numbers that you analyse are the physical values that arise in your equipment. I wonder how others come to terms with the fact that the numbers produced by the claim that sampling is the multiplication by a comb of Diracian are simply far, far too large?
Reply to
Airy R. Bean
A real sample-and-hold circuit has a finite width and a height of 1.
And the Fourier theory in actual DSP is based on discrete Fourier series, which involves integrals over finite time windows, not the continuous Fourier transform which involves integrals over all time.
And the DFT of a comb function of height 1 is another comb function of finite height. But you knew all that already, didn't you?
- Randy
Reply to
Randy Poe
Yawn and again Yawn.
The answers to the above are on google, I recall seeing you corrected on this by Dr Reay.
Reply to
Nimrod
[*Exactly* the same questions that he asked many moons ago, and which have been answered completely in these groups, with both the theoretical and practical rammifications thoroughly covered.]
You have provided no coherent or correct refutation of any of the responses that were provided in the previous discussions.
Rather than asking the same questions again, I suggest that you use groups.google.org to research the answers already provided, and post followup questions if you feel that specific clarification is necessary. Going back to your original post is unlikely to be more helpful another time around.
Reply to
Andrew Reilly
Good thing they don't claim that, but include an integrator in the idealized sampling circuit model.
- Randy
Reply to
Randy Poe
There's no problem with the mathematics involved in the delta function. You don't see the actual math in typical undergraduate courses - the exposition in a typical differential equations book is certainly far from rigorous. That's just because the rigorous explanation is not going to be accessible to that audience, not a problem with the delta function itself.
************************
David C. Ullrich
Reply to
David C. Ullrich
in article snipped-for-privacy@individual.net, Airy R. Bean at snipped-for-privacy@privacy.net wrote on 12/9/04 7:29 AM:
What is truly impossible is explaining things to Airy-head. I usually avoid dissing people, but Airy is such an inviting target.
Bill
Reply to
Repeating Rifle
Can you recommend a good website or book?
Reply to
Tim Wescott
] Rather than asking the same questions again, I suggest that you use ] groups.google.org to research the answers already provided, and post ] followup questions if you feel that specific clarification is ] necessary.Going back to your original post is unlikely to be more ] helpful another time around.
Andrew, you're assuming that understanding is the point of the exercise. I don't think it is.
Ciao,
Peter K.
Reply to
Peter K.
Why not cite some of those responses and show how they answered the questions?
The answer is, that they did not, and merely repeated parrot-fashion (or religionist fashion if you prefer) what could be read from the text books. As I referred to such textbook context initially, then those responses were meaningless, other than, perhaps, to serve as an ego-trip for the posters.
Reply to
Airy R. Bean
First of all, shame on you for lowering the tone by introducing the behavioural standards of the CBer.
That you are a CBer is indicated by your failing to realise that Ham Radio is a technical pursuit, where interest in technical development is the essence. DSP is now an increasing part of the techiques developed by _REAL_ Radio Hams and therefore any discussion relating to the understanding of DSP is entirely relevant to Ham Radio.
(You're a CBer, so you won't have a clue about what the above means, and so I append a short article to assist you.)
What is Ham Radio?
Ham Radio is a technical pursuit for those who are interested in the science of radio wave propagation and who are also interested in the way that their radios function. It has a long-standing tradition of providing a source of engineers who are born naturals.
Ham Radio awakens in its aficionados a whole-life fascination with all things technical and gives an all-abiding curiosity to improve one's scientific knowledge. It's a great swimming pool, please dive in!
This excitement causes a wish to share the experience with ones fellow man, and shows itself in the gentlemanly traditions of Ham Radio.
Radio Hams are qualified to design, build and then operate their own pieces of equipment. They do this with gusto, and also repair and modify their own equipment.
The excitement that drives a Radio Ham starts with relatively simple technologies at first, perhaps making his own Wimshurst machine and primary cells. Small pieces of test equipment follow, possibly multimeters and signal generators. Then comes receivers and transmitters. It is with the latter that communication with like-minded technically motivated people takes off. The scope for technical development grows with the years and now encompasses DSP and DDS. There is also a great deal of excitement in the areas of computer programming to be learnt and applied.
The technical excitement motivates Radio Hams to compete with each other to determine who has designed and manufactured the best-quality station. This competitiveness is found in DXing, competitions and fox-hunts.
-----OOOOO----
However, beware! A Ham Radio licence is such a desirable thing to have that there are large numbers of people who wish to be thought of as Radio Hams when, in fact, they are nothing of the kind! Usually such people are a variation of the CB Radio hobbyist; they buy their radios off the shelf and send them back to be repaired; they are not interested in technical discussion and sneer at those who are; they have no idea how their radios work inside and have no wish to find out; they are free with rather silly personal insults; they have not satisfied any technical qualification and their licences prevent the use of self-designed-and-built equipment.
These CB types engage in the competitive activities with their Cheque-Book-purchased off-the-shelf radios in a forlorn effort to prove that they are Radio Hams.
No _REAL_ Radio Hams are deceived by such people!
Reply to
Airy R. Bean
[.........]
If you think that's bad, how about the fact that signals are required to last for infinitely long in order to be correctly represented by their Fourier transform?
For a signal to be accurately represented by its Fourier transform, it must be periodic. For a signal s(t) to be periodic with period P, it must be true that s(t) = s(t + n * P) for all integral value of n (all values, including plus and minus infinite)!
So, how does anyone justify using Fourier transforms when these are clearly only valid for signals which have always been around and which will last forever!!
Outrageous !!!
Jens
PS: One professor who tried to brainwash me into accepting these Fourier transforms tried a light-hearted remark along the way that t = -innfinite was clearly going back too far - it would be enough to be gack to 1819 where H C Oersted discovered electrodynamics. Ol' HC went on the found the university I attended, but that doesn't make such rubbish slipshod pseudo-math any more valid!!!
PPS: *
Plonk*
Reply to
Jens Tingleff
There's no difficulty there because the infinite spectrum of sinusoids cancel out to zero everywhere else apart from the place at which they add constructively to produce the pulse being analysed.
That they are zero everywhere else, including the extremes of bipolar infinities means that the infinities do not feature.
Reply to
Airy R. Bean

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