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Inverse Fourier Transform

  1. May 16, 2012 #1
    Hi everyone,

    I'm trying to solve an exercise in which I need to find x(t) considering that X(ω) = cos(4ω). So, I need to find the Inverse Fourier Transform of cos(4ω), but I don't have the inverse fourier transform table.

    So, I thought about applying the duality property. If x(t) <--> X(ω), then X(t) <--> 2π*x(-ω)

    cos(4ω) <--> π[δ(ω-4) + δ(ω+4)]

    Applying the duality property

    π[δ(t-4) + δ(t+4)] <--> 2π.cos(-4ω)

    Since cos(x) = cos(-x)

    1/2*[δ(t-4) + δ(t+4)] <-->cos(4ω)


    x(t) = 1/2*[δ(t-4) + δ(t+4)]

    Is that correct? WolframAlpha is giving me a different answer :(
  2. jcsd
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