How can I apply fourier tranform to this EQ

x(t)= d/dt e^-|t|

Thank you for help

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- Dec 7th 2008, 05:19 PMlorenzoFourier transform of x(t)= d/dt e^-|t|
How can I apply fourier tranform to this EQ

x(t)= d/dt e^-|t|

Thank you for help - Dec 7th 2008, 08:14 PMmr fantastic
Here is an approach that requires minimal thinking and effort:

Theorem: $\displaystyle FT\left[ \frac{df}{dt}\right] = i \omega FT\left[ f(t) \right]$.

Theorem: $\displaystyle FT\left[ e^{-\alpha |t|} \right] = \frac{2 \alpha}{\alpha^2 + \omega^2}$.

Other approaches are possible. - Dec 7th 2008, 09:15 PMlorenzo
- Dec 7th 2008, 09:20 PMlorenzo
So, Ok you mean that the answer would be something like this thanks to the Theorems...

jwFT((2a)/(a^2+w^2)) - Dec 7th 2008, 10:28 PMmr fantastic
No. I looked at a standard table of Fourier Transforms in a textbook.

OK, I lied about the minimal thinking ..... The answer in your case is $\displaystyle j \omega \left( \frac{2}{1 + \omega^2}\right) ~ $ (since $\displaystyle \alpha = 1$).