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A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is

  1. $k \: x(t)$, where $k$ is an eigenvalue
  2. $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex exponential signal
  3. $x(t) \: e^{j \omega t}$,  where $e^{j \omega t}$ is a complex exponential signal
  4. $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system

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