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Math Help - Fourier Transform

  1. #1
    Junior Member
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    Oct 2008
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    Fourier Transform

    Hi, i need help with the following question.

    Represent by a Fourier transform the following function;

    f(x)=sin(ax)

    Thanks!
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    Right I'm currently revising this stuff too so ill give it a go...
    Is it supposed to be expressed in real form or complex?

    Heres the complex form: \sum_{n=-\infty}^{\infty} c_n e^{-inx}

    And heres the real form: \frac{a_0}{2} +  \sum_{k=1}^{\infty}(a_k cos(kx) + b_k sin(kx))

    Heres what it all means...

    c_n = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) e^{-inx} dx

    a_k = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) cos(kx) dx

    b_k = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) sin(kx) dx

    BUT... This is for when the function is 2 \pi periodic... But yours is \frac{2 \pi}{\alpha} periodic (i.e. f(x) = f(x + \frac{2 \pi}{\alpha}). So you must change the integral limit accordingly.

    If the function is odd the a_k = 0 and if its is even then b_k = 0. So as the sine function is odd... a_k = 0!

    Is this enough to start you off?
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