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Exponentials as eigenfunctions in LTI Systems

  1. Oct 19, 2007 #1
    I hope I catched the correct forum.

    Under http://en.wikipedia.org/wiki/LTI_system_theory
    e^{s t} is an eigenvalue.
    I don't really understand that the following is an eigenvalue equation:
    \quad = e^{s t} \int_{-\infty}^{\infty} h(\tau) \, e^{-s \tau} \, d \tau
    \quad = e^{s t} H(s),


    H(s) = \int_{-\infty}^\infty h(t) e^{-s t} d t .

    The integrals H(s) and \int_{-\infty}^{\infty} h(\tau) \, e^{-s \tau} \, d \tau should be unique, isn't it? So there is only one solution for H(s) = \int_{-\infty}^{\infty} h(\tau) \, e^{-s \tau} \, d \tau with one e^{s t}, isn't it?

  2. jcsd
  3. Oct 19, 2007 #2


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    [itex]F(x) = \int_a^xf(t)dt[/itex] is unique by the fundamental theorem of calculus.
    Last edited: Oct 19, 2007
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