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Help with interpolating function

  1. Mar 12, 2008 #1
    please help, i don't understand what the question is asking, please click on the thumbnail for the question.
     

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  3. Mar 12, 2008 #2

    rbj

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    hxluo, you need to learn how to use LaTeX here so you can post math equations that we can cut, copy, or paste in our discussion with you.

    i think there is a mistake in the question. it needs to read:

    _________

    Let x(t) be a bandlimited signal such that

    [tex] X(j \omega) = 0 \quad \forall \quad |\omega| \ge \frac{\pi}{T} [/tex]
    _________

    i think the little t should be a capital T in the denominator of that fraction.
     
  4. Mar 12, 2008 #3
    yes you are right, so how do i solve this problem?
     
  5. Mar 12, 2008 #4

    rbj

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    okay, you know about Laplace or Fourier Transformation, right?

    [tex] X(s) = \int_{-\infty}^{+\infty} x(t) e^{-st} dt [/tex]

    this is the same X(.) as in

    [tex] X(j \omega) = 0 \quad \forall \quad |\omega| \ge \frac{\pi}{T} [/tex] .

    and, from the nature of the problem, you know about the Nyquist/Shannon Sampling and Reconstruction Theorem, right? so if the differentiator wasn't there, how would you come up with an interpolation relationship for reconstructing

    [tex] x(t) = \sum_{n=-\infty}^{\infty} x(nT) h(t - nT) [/tex] ?

    what is "h(t)"?
     
  6. Mar 15, 2008 #5
    i just don't understand the concept of interpolation that much.
     
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