4.2.5. Eigenfunctions of LTI systemΒΆ
\(\newcommand{\op}[1]{\mathsf #1}\) \(\newcommand{\ztarrow}{\stackrel{\op Z}{\longrightarrow}}\)
The function \(x[n] = z^{n}\) is an eigenfunction of a LTI system, i.e.
\[z^{n} \ast h[n] \ztarrow H(z) z^{n}\]
\(\newcommand{\op}[1]{\mathsf #1}\) \(\newcommand{\ztarrow}{\stackrel{\op Z}{\longrightarrow}}\)
The function \(x[n] = z^{n}\) is an eigenfunction of a LTI system, i.e.