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Math Help - Fourier transforms

  1. #1
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    Fourier transforms

    How is it possible to recover u(x) given the its fourier transform v(\omega) and the inverse transform? by using the definition?

    v(\omega) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{-iwx}{u(x)}{dx}

    u(x) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{iwx}{v(\omega)}{d\omega}

    is there some sort of change of variables that needs to be done?

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bchanyi View Post
    How is it possible to recover u(x) given the its fourier transform v(\omega) and the inverse transform? by using the definition?

    v(\omega) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{-iwx}{u(x)}{dx}

    u(x) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{iwx}{v(\omega)}{d\omega}

    is there some sort of change of variables that needs to be done?

    Thanks
    I don't understand your question. You give the transform pair which tells
    you how to find the FT of a function and how to recover the original function
    from the transform (at least for functions for which these integrals have
    meaning).

    RonL
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  3. #3
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    how do you sub v(w) into u(x) to recover u(x) back so that u(x)= u(x) to prove that that is the inversion formula. how can you do that? what manipulation are you suppose to do?
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