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Fourier problem

  1. Apr 10, 2006 #1
    I am trying to solve this fourier problem where I have to integrate
    ∫f(x) * exp(-i§x) dx from -∞ to ∞ , where f(x) = exp(-sgn(x))
    I tried breaking the function into two pieces where x is from -∞ to 0 and from 0 to ∞ where f(x) would then be exp(x) and exp(-x) and integrating two functions, but that didn't seem to be working. The the other way I can think of is trying to integrate
    exp(-i§x) * exp(-sgn(x)), but I'm not sure if that is possible. Could anyone please give me a hint?
  2. jcsd
  3. Apr 10, 2006 #2


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    Homework Helper

    What is § ? a constant, an operator, or a function?
  4. Apr 10, 2006 #3
    it is (n*PI)/L ,where 2L is one period which I just treat as a constant
  5. Apr 10, 2006 #4


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    L is one period of what? If your function, f, is periodic, then you need only integrate over one period. In that case, you are talking about a Fourier Series, not a Fourier transform and probably would find it easier to use [itex]sin(\frac{n\pi}{L}t)[/itex] and [tex]cos(\frac{n\pi}{L}t)[/itex] rather than complex exponentials.

    If is not periodic, then you need the Fourier transform [itex]\int_{-infty}^\infty f(x)e^{-ixt}dt[/itex].
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