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Homework Help: E^x integration

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi, I need to find the spectrum of the following function:
    [tex]i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1][/tex]

    2. Relevant equations
    the Fourier Transform would be:
    [tex]\int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]e^{-j2\pi ft}dt[/tex]

    3. The attempt at a solution
    I'm not sure where to start because I'm not sure how to take the integral of an exponential when there is a trig term in there. Is this integral even possible or would it diverge to infinity?

    Hope you guys can help,
  2. jcsd
  3. May 28, 2010 #2
    I think I worked it out! I need to express the exp(x) function as a taylor series, and as n gets larger (greater than say 3) the number approaches 0! So you can approximate it up to n=3 and then integration should be ok.
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