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Impossible sampling theory!

Discussion in 'Electrical Engineering' started by Airy R. Bean, Dec 9, 2004.

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  1. Airy R. Bean

    Airy R. Bean Guest

    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?
     
  2. Airy R. Bean

    Airy R. Bean Guest

    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.
     
  3. Airy R. Bean

    Airy R. Bean Guest

    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?
     
  4. Airy R. Bean

    Airy R. Bean Guest

    The only trolls in this NG would seem to be those
    who clamour that the troll should not be fed. Often, as
    in the case of Westcott below, their plaintiff moans
    follow their showing themselves up with childish
    outbursts which are then chastised without being risen
    to.

    Having been so chastised, they try to suggest that it is others
    rather than they themselves as the originators of
    childish posts who should be ostracised.
     
  5. deBaser

    deBaser Guest

    Hey a troll is for life not just for xmas. Do you know there are starving
    trolls out there so give him all your [email protected]' money. Feed the troll, let
    him know its xmas time

    Bob Geldoff
     
  6. Airy R. Bean

    Airy R. Bean Guest

    How tall do you think it is for the multiplication
    to take effect in a real circuit?
     
  7. One of my professors implied that the Dirac delta wasn't mathematically
    rigorous but provides correct results so it's used nonetheless.
     
  8. James Bond

    James Bond Guest

    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
     
  9. You mean "plaintive".
     
  10. Airy R. Bean

    Airy R. Bean Guest

    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?
     
  11. Airy R. Bean

    Airy R. Bean Guest

    Yes! I did!

     
  12. Peter

    Peter Guest

    he's thinking he's in court once again!
     
  13. Nimrod

    Nimrod Guest

    Yawn and again Yawn.

    The answers to the above are on google, I recall seeing you corrected on
    this by Dr Reay.
     
  14. On Thu, 09 Dec 2004 16:29:52 +0000, Airy R. Bean wrote:
    [*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.
     
  15. Airy R. Bean

    Airy R. Bean Guest

    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.
     
  16. Airy R. Bean

    Airy R. Bean Guest

    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!
     
  17. Airy R. Bean

    Airy R. Bean Guest

    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.
     
  18. You are confusing Fourier series with Fourier transform.
    Nonsense. You are confusing Fourier series with Fourier transform.
    Nonsense. You are confusing Fourier series with Fourier transforms.
    Yup.
     
  19. Gareth, this really is ridiculous. So many people have posted answers
    to you that it isn't practical to even know where to start. You, on
    the other hand, are the one claiming they're incorrect, so the burden
    really is on you to explain why you think so.
    This just oozes irony. Gushes. Floods.

    Eric Jacobsen
    Minister of Algorithms, Intel Corp.
    My opinions may not be Intel's opinions.
    http://www.ericjacobsen.org
     
  20. Better watch out, Gareth, there's a guy here who hates it when people
    post childish personal insults. You don't want to get on his bad
    side.


    Eric Jacobsen
    Minister of Algorithms, Intel Corp.
    My opinions may not be Intel's opinions.
    http://www.ericjacobsen.org
     
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