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one the problems from my book, states the following:

Find the Fourier Transform of:

a) $$\frac{1}{2\pi(a-jt)^2}$$

the solution for it is -> \$\omega e^{-a\omega} \mathrm{u}(\omega)\$

I know there exist a relation such that \$1/(a+jt)^2\$ is F.T of \$te^{-at} \mathrm{u}(t)\$. what happens to the \$1/2\pi\$ part? I don't understand how they manipulate it such that they are able to use the Fourier Table they have in the book.

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  • \$\begingroup\$ In your equation, is "pi" the number 3.14... or the square pulse function? \$\endgroup\$
    – The Photon
    May 11, 2016 at 5:18
  • \$\begingroup\$ @ThePhoton If it was the square pulse function, the x² squaring would not make much sense. :) \$\endgroup\$
    – pipe
    May 11, 2016 at 7:42
  • \$\begingroup\$ I've made an edit to the question to add mathematical formatting and to attempt to clarify. Please verify that the equations are what you intended. \$\endgroup\$
    – Edward
    May 11, 2016 at 11:29

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I haven't been doing math for a long time. Though I think you've already found most of the answer.

I don't remember all the Fourier tables but if what you say is correct, then if you suppose that ω = 2πf you finally have your solution.

\$2πf e^{-2πfa} \mathrm{u}(f)\$ which is \$\omega e^{-\omega a} \mathrm{u}(\omega)\$

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