(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using properties of the Fourier transform, calculate the Fourier transform of: sgn(x)*e^(-a*abs(x-2))

2. Relevant equations

FT(f(x))= integral from -∞ to +∞ of f(x)*e^(-iwx) dx

3. The attempt at a solution

I've realised that with the signum function, the boundaries of the integral can be reduced to: integral from 0 to 4 of e^(-a*abs(x-2))*e^(-iwx) dx from 0 to 4. However I'm guessing that I just can't use the properties and theorems related to fourier transforms as the integral does not have the same boundaries as the original... Maybe I just souldn't have changed the integral...Any help?

Sorry for not using latex I really don't understand it =/

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# Fourier transform of signum function*exponential

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