- #1

gony rosenman

- 11

- 4

## Homework Statement

find the Fourier transform of the following function in

__two ways__, once using direct computation , and second using the convolution therom .

## Homework Equations

_{0}t)/(d

^{2}+t

^{2})

## The Attempt at a Solution

I tried first to solve directly . used Euler's identity and got

∫e

^{-it(w0+w)}/(d

^{2}+t

^{2}) + ∫e

^{it(w0-w)}/(d

^{2}+t

^{2})

but I think it was a deadend , unsolvable integral .

I got a hint from an internet source saying to use the Lorentzian transform but I am not familiar with it

then I tried going first from the convolution approach , which means I find the separate F transform of cos(w

_{0}t) and of 1/(d

^{2}+t

^{2}) and then calculate the convolution of them in order to get the FT of the multiplication oh them .

I couldn't do that as well because I didn't manage to integrate e

^{-iwt}/(d

^{2}+t

^{2}) and so can't find that Fourier transform as well

any direction ,or explained hint would be greatly appreciated!

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