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Fourier Intergrals and transforms

  1. Nov 13, 2006 #1
    How do I do a Fourier integral (and whats the point of them??)

    I've been asked to evaluate

    [tex]F(\omega) = \frac{1}{\sqrt{2\pi}}\int dte^{-\alpha t}cos\omega t[/tex]

    and I've not the foggiest idea what to do. I thought I could just go about doing in the integral by parts (limits are 0 and infinity by the way), but on further research I don't think I can do that can I?
  2. jcsd
  3. Nov 13, 2006 #2
    Try integration by parts.
  4. Nov 14, 2006 #3


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    Substitute into your integral and you will have the sum of two exp integrals. I presume you can do that.
  5. Nov 14, 2006 #4
    Yes thats familliar. I have done this integral before - just never dawned on me to use the substitution.

    I was also a little confused when it called it a Fourier Integral. I thought it was going to be a lot more complex than it appears to be now.
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