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Inverse fourier transform of constant

  1. Mar 19, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the inverse fourier transform of f(w)=1 Hint: Denote by f(x) the inverse fourier transform of 1 and consider convolution of f with an arbitrary function.


    2. Relevant equations

    From my textbook the inverse fourier transform of f(w)=[itex]\int[/itex] F(w)e^-iwt dw


    3. The attempt at a solution

    Ive tried letting f(x) be the fourier transform of 1 and convolving it with an arbitrary function g(x) but for some reason this leads me nowhere.
     
  2. jcsd
  3. Mar 19, 2014 #2

    SammyS

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    Precisely what sort of nowhere do you get to?
     
  4. Mar 19, 2014 #3
    i let f(x)= Inverse fourier transform of 1, which from the formula i have gives f(x)=∫e^-iwx dw

    then using the convolution formula with my f(x) above and the aribitrary function g(x) i get

    f*g(x) = ∫e^-iwx dw ∫ g(x-t) dt

    the integrals have bounds -∞ to ∞
     
  5. Mar 20, 2014 #4
    ive got it solved now. thanks anyways sammy! :)
     
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