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Computing Fourier transforms with exponentials

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Compute the Fourier transform of f(x)=exp(-b|x|), b>0

    2. Relevant equations

    F(k)=1/2pi(integral[inf,-inf]f(x)exp(ikx)dx)

    3. The attempt at a solution

    F(k)=1/2pi(integral[inf,-inf]exp(ikx-b|x|)

    How do I solve this? I've tried to solve it but can't get to a solution because of the modulus sign.
     
  2. jcsd
  3. Mar 26, 2012 #2
    write the integral as sum of two integrals and integrate each one of them.
     
  4. Mar 28, 2012 #3
    Thank you!
     
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