What is the Fourier Transform of
f(t) = A(e^(-at)-e^(-b*t))?
Typing it into Wolfram Alpha you get:
sqrt(2 pi) C delta(i a+omega)-sqrt(2 pi) C delta(i b+omega)
Question 1) Is this correct?
Question 2) What is a delta function when argument is complex?
What is stopping me from using this solution to solve the problem. I.e:
Ft(w) = (A/Pi) (-a/Pi/(w^2 + (a/Pi)^2) - -b/Pi/(w^2 + (b/Pi)^2))
Question 3) What is the significance of k0 with reference to k? Or is k0 just a constant?