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+\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 0.9.1 - 24.09.2012} \maketitle \newpage @@ -519,7 +519,8 @@ Das Spektrum eines Realen Zufallsprozesses ist komplett im Intervall $[0,\pi]$ b \chapter{Filter} \section{Lineare Filter} Wenn $X(n)$ und $Y(n)$ \emph{stationr} (\ref{stationarystrict}) sind, $h(n)$ eine Impulsantwort eines LTI-Systems ist - und das Filter \emph{stabil} (\ref{Stability}) ist, existiert mit \emph{Wahrscheinlichkeit 1} (\ref{conv:one}) + und das Filter \emph{stabil} (\ref{Stability}) ist, existiert mit \emph{Wahrscheinlichkeit eins} (\ref{conv:one}) + das lineare Filter mit: \begin{equation} \label{eq:linfil} Y(n)=\sum\limits_{k=-\infty}^\infty h(k)X(n-k)=\sum\limits_{k=-\infty}^\infty h(n-k)X(k) \end{equation} @@ -530,6 +531,7 @@ Die Stabilit \end{equation} \subsection{Eigenschaften eines Linearen Filters} +Die folgenden Eigenschaften gelten nur, wenn das Filter \emph{stabil} (\ref{Stability}) ist \begin{itemize} \item Ist $X(n)$ \emph{stationr} (\ref{stationarystrict}) und $\E[|X(n)|]<\infty$, dann ist $Y(n)$ \emph{stationr} \item $Y(n)$ wird linearer Prozess genannt (linear process)