1.1 --- a/doc-src/isac/jrocnik/present-1.tex Fri Jul 22 12:10:21 2011 +0200
1.2 +++ b/doc-src/isac/jrocnik/present-1.tex Sat Jul 23 18:46:38 2011 +0200
1.3 @@ -151,6 +151,8 @@
1.4 {\footnotesize\it
1.5 Fourier Transform
1.6
1.7 +\hrulefill
1.8 +
1.9 \begin{tabbing}
1.10 1\=postcond \=: \= \= $\;\;\;\;$\=\kill
1.11 \>given \>:\> Time continiues, not periodic Signal \\
1.12 @@ -162,13 +164,6 @@
1.13
1.14 }
1.15 \end{frame}
1.16 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.17 -%% Transform expl 1 CALC %%
1.18 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.19 -
1.20 -\begin{frame}\frametitle{Fourier Transformation 1: Calculation}
1.21 -TODO: Bernhard fragen ob Tabelle oder Rechnung
1.22 -\end{frame}
1.23
1.24 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.25 %% Transform expl 1 REQ %%
1.26 @@ -226,38 +221,6 @@
1.27 \end{frame}
1.28
1.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.30 -%% Transform expl 2 CALC %%
1.31 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.32 -
1.33 -%\begin{frame}\frametitle{Fourier Transform 2: Calculation}
1.34 -%\footnotesize{
1.35 -%\begin{tabbing}
1.36 -%000\=\kill
1.37 -%01 \> ${\cal F}\;(x(t-2)) =$\\
1.38 -% \`${\cal F}\;(x(t-T)) = e^{-j\cdot\omega\cdot T}\cdot X\;j\cdot\omega$\\
1.39 -%02 \> $e^{-j\cdot\omega\cdot 2}\cdot X\;(j\cdot\omega)$\\
1.40 -% \`definition $X\;(j\cdot\omega)$\\
1.41 -%03 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-\infty}^\infty x\;t\;\cdot e^{-j\cdot\omega\cdot t} d t$\\
1.42 -% \` $x\;t = 1\;{\it for}\;\{x.\;-1\leq t\;\land\;t\leq 1\}\;{\it and}\;x\;t=0\;{\it otherwise}$\\
1.43 -%04 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-1}^1 1\cdot e^{-j\cdot\omega\cdot t} d t$\\
1.44 -% \` $\int_a^b f\;t\;dt = \int f\;t\;dt\;|_a^b$\\
1.45 -%05 \> $e^{-j\cdot\omega\cdot 2}\cdot \int 1\cdot e^{-j\cdot\omega\cdot t} d t\;|_{-1}^1$\\
1.46 -% %\` $\int e^{a\cdot t} = \frac{1}{a}\cdot e^{a\cdot t}$\\
1.47 -% \` pbl: integration in $\cal C$\\
1.48 -%06 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot t} \;|_{-1}^1)$\\
1.49 -% \` $f\;t\;|_a^b = f\;b-f\;a$\\
1.50 -%07 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot 1} - \frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot -1})$\\
1.51 -%\vdots\` pbl: simplification+factorization in $\cal C$\\
1.52 -%08 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{-j\cdot\omega}\cdot(e^{j\cdot\omega} - e^{-j\cdot\omega})$\\
1.53 -% \` trick~!\\
1.54 -%09 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{\omega}\cdot(\frac{-e^{j\cdot\omega} + e^{-j\cdot\omega}}{j})$\\
1.55 -% \` table\\
1.56 -%10 \> $e^{-j\cdot\omega\cdot 2}\cdot 2\cdot\frac{\sin\;\omega}{\omega}$
1.57 -%\end{tabbing}
1.58 -%}
1.59 -%\end{frame}
1.60 -
1.61 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.62 %% Transform expl 2 REQ %%
1.63 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.64
1.65 @@ -283,8 +246,6 @@
1.66 %%--------------------FOURIER---Conclusion-----------------------%%
1.67 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.68
1.69 -%\subsection[Summary]{Summary}
1.70 -
1.71 \begin{frame}{Summary}
1.72 todo
1.73
1.74 @@ -303,7 +264,7 @@
1.75 \subsection[Convolution]{Convolution}
1.76
1.77 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.78 -%% DTS INTRO %%
1.79 +%% LTI INTRO %%
1.80 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.81
1.82 \begin{frame}\frametitle{Convolution: Introduction}
1.83 @@ -317,7 +278,7 @@
1.84 \end{frame}
1.85
1.86 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.87 -%% DTS SPEC %%
1.88 +%% LTI SPEC %%
1.89 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.90
1.91 \begin{frame}\frametitle{Convolution: Specification}
1.92 @@ -332,6 +293,8 @@
1.93
1.94 The two systems are cascaded seriell. Derive the impulse respinse of the overall system $h_c[n]$.
1.95
1.96 +\hrulefill
1.97 +
1.98 \begin{tabbing}
1.99 1\=postcond \=: \= \= $\;\;\;\;$\=\kill
1.100 \>given \>:\> Signals h1[n], h2[n] \\
1.101 @@ -346,15 +309,7 @@
1.102 \end{frame}
1.103
1.104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.105 -%% DTS CALC %%
1.106 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.107 -
1.108 -%\begin{frame}\frametitle{Convolution: Calculation}
1.109 -%TODO
1.110 -%\end{frame}
1.111 -
1.112 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.113 -%% DTS REQ %%
1.114 +%% LTI REQ %%
1.115 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.116
1.117 \begin{frame}\frametitle{Convolution: Development effort}
1.118 @@ -375,6 +330,21 @@
1.119 effort --- in 45min units\\
1.120 }
1.121 \end{frame}
1.122 +
1.123 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.124 +%%--------------------LTI-------Conclusion-----------------------%%
1.125 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.126 +
1.127 +\begin{frame}{Summary}
1.128 +todo
1.129 +
1.130 +\begin{itemize}
1.131 +
1.132 +\item todo
1.133 +
1.134 +\end{itemize}
1.135 +\end{frame}
1.136 +
1.137 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.138 %-----------------------------------------------------------------%
1.139 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.140 @@ -393,17 +363,11 @@
1.141 \end{itemize}
1.142 \end{frame}
1.143
1.144 -% does not fit?!
1.145 -%\subsection[]{Indextranformation}
1.146 -%\begin{frame}\frametitle{TODO}
1.147 -%TODO
1.148 -%\end{frame}
1.149 -
1.150 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.151 %% Z-Transform SPEC %%
1.152 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.153
1.154 -\begin{frame}\frametitle{(Inverse) ${\cal Z}$-Transformation: Specification}
1.155 +\begin{frame}\frametitle{(Inverse) Z-Transformation: Specification}
1.156 {\footnotesize\it
1.157
1.158 Determine the inverse $\cal{z}$ transform of the following expression. Hint: applay the partial fraction expansion.
1.159 @@ -412,6 +376,8 @@
1.160 $X(z)=\frac{3}{z-\frac{1}{4}-\frac{1}{8}z^{-1}},\ \ x[n]$ is absolute summable
1.161 \end{center}
1.162
1.163 +\hrulefill
1.164 +
1.165 \begin{tabbing}
1.166 1\=postcond \=: \= \= $\;\;\;\;$\=\kill
1.167 \>given \>:\> Expression of z \\
1.168 @@ -426,19 +392,11 @@
1.169 \end{frame}
1.170
1.171 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.172 -%% Z expl CALC %%
1.173 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.174 -
1.175 -%\begin{frame}\frametitle{(Inverse) ${\cal Z}$-Transformation: Calculation}
1.176 -%TODO
1.177 -%\end{frame}
1.178 -
1.179 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.180 %% Z expl REQ %%
1.181 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.182
1.183
1.184 -\begin{frame}\frametitle{(Inverse) ${\cal Z}$-Transformation: Development effort}
1.185 +\begin{frame}\frametitle{(Inverse) Z-Transformation: Development effort}
1.186 {\small
1.187 \begin{center}
1.188 \begin{tabular}{l|l|r}
1.189 @@ -462,6 +420,20 @@
1.190 }
1.191 \end{frame}
1.192
1.193 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.194 +%%--------------------Z-TRANS---Conclusion-----------------------%%
1.195 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1.196 +
1.197 +\begin{frame}{Summary}
1.198 +todo
1.199 +
1.200 +\begin{itemize}
1.201 +
1.202 +\item todo
1.203 +
1.204 +\end{itemize}
1.205 +\end{frame}
1.206 +
1.207 \end{document}
1.208
1.209