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Math Help - Fourier transformation

  1. #1
    Ase
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    Fourier transformation

    Hi

    I am trying to calculate the Fourier transformation of the function

    f(x)=exp(-x)*(the characteristic function running from 0 to 1, both included)

    what I have got so far is this

    |f_hat(gamma)|=|int_from -infinty to infinity (f(x)*exp(-2*pi*i*x*gamma)dx)|

    = int_o to 1(exp(-x)*exp(-2*pi*i*x*gamma)dx)

    and then what? Have I made a mistake somewhere along the way or is it simply a case of having got stuck?

    thanks in advance
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  2. #2
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    Quote Originally Posted by Ase View Post
    Hi

    I am trying to calculate the Fourier transformation of the function

    f(x)=exp(-x)*(the characteristic function running from 0 to 1, both included)

    what I have got so far is this

    |f_hat(gamma)|=|int_from -infinty to infinity (f(x)*exp(-2*pi*i*x*gamma)dx)|

    = int_o to 1(exp(-x)*exp(-2*pi*i*x*gamma)dx)

    and then what? Have I made a mistake somewhere along the way or is it simply a case of having got stuck?

    thanks in advance
    Then what ....? Use a well known index law to write the integrand in the form e^{kx} and then integrate.
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  3. #3
    Ase
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    Hi mrfantastic

    I am well aware of the index law. The "then what" referred to what happens to the gamma. I can only integrate over x but what happens to gamma?
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  4. #4
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    Quote Originally Posted by Ase View Post
    Hi mrfantastic

    I am well aware of the index law. The "then what" referred to what happens to the gamma. I can only integrate over x but what happens to gamma?
    The integral is respect to x so gamma is treated as a constant as far as the integration is concerned. So the result of the integration is a function of gamma, which ought to be no surprise.
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  5. #5
    Ase
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    Ok. Thanks a lot. I was just under the impression that the end result should be a number (not a function).
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