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Math Help - Fourier transform

  1. #1
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    Fourier transform

    The problem is:

    Find the fourier transform of:

    f(t)=\int{cos(t)*e^{-t^2}}

    My question is: can i solve this problem using convolution, and how? I have some problems understanding when to apply convolution, can I choose
    f(t)=g(t)*h(t) with g(t)=cos(t) and h(t)=e^{-t^2}, and then say that F(f) = F(g*h) = \sqrt{2*Pi}*F(g)*F(h) ?
    Or is this completely wrong?
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  2. #2
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    Quote Originally Posted by dreamsound View Post
    The problem is:

    Find the fourier transform of:

    f(t)=\int{cos(t)*e^{-t^2}}

    My question is: can i solve this problem using convolution, and how? I have some problems understanding when to apply convolution, can I choose
    f(t)=g(t)*h(t) with g(t)=cos(t) and h(t)=e^{-t^2}, and then say that F(f) = F(g*h) = \sqrt{2*Pi}*F(g)*F(h) ?
    Or is this completely wrong?
    Is f(t)=\int{cos(t)*e^{-t^2}} meant to repesent the convolution of \cos(t) and e^{-t^2} ? (Your notation is poor if that's the case). If so, there is a standard operational theorem for finding the Fourier transform of the convolution of two functions.

    Otherwise, please post the question exactly as it's worded and with the exact notation used.
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  3. #3
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    Sorry, i now see that my notation might be confusing.

    A better notation is:
    f(t)=\int{cos(t)e^{-t^2}}
    i.e. it's just ordinary multiplication...
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