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Tyde 2013-02-15 11:59:48 +01:00
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@ -23,7 +23,7 @@
\title{Stochastische Signale und Systeme}
\subtitle{Zusammenfassung Formeln}
\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 1.0 - 27.09.2012}
\subsubtitle{Autor: Daniel Thiem - studium@daniel-thiem.de\\Version 1.1 - 15.02.2013}
\maketitle
\newpage
@ -244,7 +244,7 @@ P \left(\lim_{k\rightarrow\infty} |X_k-X|=0\right)=1
\end{itemize}
\chapter{Discrete-Time-Fourier-Transformation}
\section{Abtastung}
\section{Abtastung} \label{fouriersampling}
\subsection{Im Zeitbereich}
Sei $x_c(t)$ das zu abtastende Signal und $T_s=\frac{1}{f_s}$ die Abtastdauer bzw. Abtastfrequenz
\begin{equation}
@ -627,7 +627,7 @@ c_{YX}&=\int\limits_{-\pi}^\pi H\freq C_{XX}\freq e^{-j\omega\kappa}\frac{d\omeg
\begin{subequations}
\begin{align}
c_{Y_1Y_2}(\kappa)&=\sum\limits_{k=-\infty}^\infty \sum\limits_{l=-\infty}^\infty h_1(k)h_2(l)\cdot c_{X_1X_2}(\kappa -k+l) \\
c_{Y_1Y_2}(\kappa)&=\sum\limits_{k=-\infty}^\infty \sum\limits_{l=-\infty}^\infty h_1(k)h_2(l)^*\cdot c_{X_1X_2}(\kappa -k+l) \\
c_{Y_1Y_2}(\kappa)&=h_1(\kappa)\star h_2(\kappa)^*\star c_{X_1X_2}(\kappa)\\
C_{Y_1Y_2}\freq &=H_1\freq H_2\freq^*C_{X_1X_2}\freq
\end{align}