I am having problems finding the inverse Fourier transform of:


I think I could use convolution property but I'm stuck. I know that:

$$ f(t) = e^{-at} H(t) \implies f(w) = \frac{1}{(a+iw)}$$

Can somebody help me?

  • 5
    $\begingroup$ Use partial fraction expansion $\endgroup$ – Mark Viola Jul 5 '18 at 23:15
  • $\begingroup$ Thanks so much! $\endgroup$ – emee Jul 5 '18 at 23:32
  • $\begingroup$ You're welcome. My pleasure $\endgroup$ – Mark Viola Jul 6 '18 at 2:45

We write




Then we have

$$A+B=0$$ $$2A+B=1$$

$$A=1$$ $$B=-1$$




Where $u(t)$ is the Heaviside function

Note: there may be a constant of $\sqrt{2\pi}$ depending on conventions being used


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