Eigenfunctions of LTI system
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$\newcommand{\op}[1]{\mathsf #1}$
$\newcommand{\ztarrow}{\stackrel{\op Z}{\longrightarrow}}$


The function $x[n] = z^{n}$ is an eigenfunction of a LTI system, i.e.

.. math::
   z^{n} \ast h[n] \ztarrow H(z) z^{n}