I hope I catched the correct forum.(adsbygoogle = window.adsbygoogle || []).push({});

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),

where

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?

Thanks

Tanja

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# Exponentials as eigenfunctions in LTI Systems

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