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Math Help - Fourier transform of x(t)= d/dt e^-|t|

  1. #1
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    Fourier 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
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  2. #2
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    Quote Originally Posted by lorenzo View Post
    How can I apply fourier tranform to this EQ

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

    Thank you for help
    Here is an approach that requires minimal thinking and effort:

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

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


    Other approaches are possible.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Here is an approach that requires minimal thinking and effort:

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

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


    Other approaches are possible.

    Hey,.... Did you get to use any software to obtain this particular solution?
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    So, Ok you mean that the answer would be something like this thanks to the Theorems...

    jwFT((2a)/(a^2+w^2))
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  5. #5
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    Quote Originally Posted by lorenzo View Post
    Hey,.... Did you get to use any software to obtain this particular solution?
    No. I looked at a standard table of Fourier Transforms in a textbook.

    Quote Originally Posted by lorenzo View Post
    So, Ok you mean that the answer would be something like this thanks to the Theorems...

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