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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(x2))
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(x2))*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 =/
Using properties of the Fourier transform, calculate the Fourier transform of: sgn(x)*e^(a*abs(x2))
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(x2))*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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