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Fourier transform of ODE

  1. Nov 27, 2005 #1
    we need to find the F.T of
    f(t) = 0 for t<0
    f(t) = exp(-at) for t>=0
    where a is a real positive constant
    and F(w) = the integral w.r.t t between minus infinity and plus infinity of [exp(iwt)*f(t)]

    which turns out to be 1/(a-iw)

    we now have the ODE L*dI/dt + RI = f(t)
    where L,R are constants represeting resistance and inductance. we need to show that the fourier transform of I(t) is 1/(a-iw)(R-Liw) which is again straightforward. We need to find I(t). I have sepearated the F.T of I(t) using partial fractions and used the inverse fourier transform, but I'm not sure how to evaluate the integrals.
    thanks very much for your help
     
  2. jcsd
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