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Fourier transform

  1. Oct 26, 2004 #1
    hi ,

    the question is to find the fourier transform of the following eqn without using integration

    d(t)= [c(-1.5t)]exp(jwat)

    where
    c(t)= Ao + E(Sumation)An*cos(nwot) + Bn sin(nwot) [fourier series formula]

    I knwo to find the FT of the above fourier series. But why is exp(jwat)
    the frequency shift and why shud we shift by wa.

    Thanks,
    skan
     
  2. jcsd
  3. Oct 26, 2004 #2

    NateTG

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    Science Advisor
    Homework Helper

    Please don't cross/double post.

    I'm assuming that:
    [tex]j=\sqrt{-1}[/tex]
    since you're a phyicist.

    Then if you apply the euler equation:
    [tex]e^{j\theta}=\cos \theta + j \sin \theta[/tex]

    you should see how the exponent affects the frequency.
     
  4. Oct 26, 2004 #3
    Sorry for the double post.

    1.Thanks but I take the FT of c(t) first and then I shift all the impulse functions by wa.
    can someone please explain why as i dont understand why this is done this way.

    2.Also I thought that the Integral of an impulse function is 1, but here its says that the integral of a impulse function is a unit step function.

    thanks
     
  5. Oct 26, 2004 #4
    I mean I read in my notes that the integral of a impulse function is a unit step function
     
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