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Inverse Fourier Transform and Power Signals

  1. Oct 25, 2012 #1
    I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem:

    Question: Given the fourier transform of an aperiodic signal

    X(ω) = 2*sin(3(ω-2π))/ω-2π

    (a)find its inverse fourier transform x(t) using only tables and properties
    (b) find the power of the signal x(t)


    I know that I have to preform Frequency shift property involving the 2π and I have to preform the scaling property for the 3. I also know that I can use the relationship

    sin(τω)/ω = τsinc(τω/2)

    and the inverse fourier transform of
    τsinc(τω/2) → ∏(t/τ)

    The problem I am having is understanding how to perform the frequency shift and the scaling property in order to get X(ω) into the form of sin(τω)/ω so i can preform the inverse fourier transform. from there the power is equal to x^2(t) which is equal to the

    lim T→∞ of ∫ g^2(t)dt from -T/2 to T/2
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 26, 2012 #2
    You should look at replacing w with something else so that X(w+?) generates the sin(ax)/x term.

    The signal is not periodic so I think you misspoke -- it doesn't make sense to speak about power for aperiodic signals so I think you meant energy. Subtle, I know, but it's important to keep it straight :)
     
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