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Computing Fourier transforms with exponentials

  • Thread starter js10j2jh
  • Start date
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.
 
write the integral as sum of two integrals and integrate each one of them.
 
Thank you!
 

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