1.1 --- a/doc-src/isac/jrocnik/present-1.tex	Thu Jul 07 10:29:12 2011 +0200
     1.2 +++ b/doc-src/isac/jrocnik/present-1.tex	Thu Jul 07 16:09:17 2011 +0200
     1.3 @@ -139,19 +139,36 @@
     1.4  \end{frame}
     1.5  
     1.6  \subsection[Transform]{Fourier transform}
     1.7 -\begin{frame}\frametitle{Fourier transform expl 1}
     1.8 +\begin{frame}\frametitle{FT expl 1}
     1.9  TODO
    1.10  \end{frame}
    1.11  
    1.12 -\begin{frame}\frametitle{Fourier transform expl 2a}
    1.13 +\begin{frame}\frametitle{FT expl 2a}
    1.14  TODO
    1.15  \end{frame}
    1.16  
    1.17 -\begin{frame}\frametitle{Fourier transform expl 2b}
    1.18 -Aufgabenstellung von Bernhard
    1.19 +\begin{frame}\frametitle{FT expl 2b}
    1.20 +Problem (from Bernhard)
    1.21  \end{frame}
    1.22  
    1.23 -\begin{frame}\frametitle{Fourier transform expl 2b}
    1.24 +\begin{frame}\frametitle{FT expl 2b: specification }
    1.25 +{\footnotesize\it
    1.26 +fourier transform
    1.27 +\begin{tabbing}
    1.28 +1\=postcond \=: \= \= $\;\;\;\;$\=\kill
    1.29 +\>given    \>:\>  piecewise\_function \\
    1.30 +\>         \> \>  \>$(x (t::real), [(0,-\infty<t<1), (1,1\leq t\leq 3), (0, 3<t<\infty)])$\\
    1.31 +                        %?(iterativer) datentyp in Isabelle/HOL
    1.32 +\>         \> \>  translation $T=2$\\
    1.33 +\>precond  \>:\>  TODO\\
    1.34 +\>find     \>:\>  $X(j\cdot\omega)$\\
    1.35 +\>postcond \>:\>  TODO\\
    1.36 +\end{tabbing}
    1.37 +
    1.38 +}
    1.39 +\end{frame}
    1.40 +
    1.41 +\begin{frame}\frametitle{FT expl 2b: calculation}
    1.42  \footnotesize{
    1.43  \begin{tabbing}
    1.44  000\=\kill
    1.45 @@ -164,11 +181,12 @@
    1.46  04 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-1}^1 1\cdot e^{-j\cdot\omega\cdot t} d t$\\
    1.47        \` $\int_a^b f\;t\;dt = \int f\;t\;dt\;|_a^b$\\
    1.48  05 \> $e^{-j\cdot\omega\cdot 2}\cdot \int 1\cdot e^{-j\cdot\omega\cdot t} d t\;|_{-1}^1$\\
    1.49 -      \` $\int e^{a\cdot t} = \frac{1}{a}\cdot e^{a\cdot t}$\\
    1.50 +      %\` $\int e^{a\cdot t} = \frac{1}{a}\cdot e^{a\cdot t}$\\
    1.51 +       \` pbl: integration in $\cal C$\\
    1.52  06 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot t} \;|_{-1}^1)$\\
    1.53        \` $f\;t\;|_a^b = f\;b-f\;a$\\
    1.54  07 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot 1} -  \frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot -1})$\\
    1.55 -\vdots\` simplification+factorization in $\cal C$\\
    1.56 +\vdots\` pbl: simplification+factorization in $\cal C$\\
    1.57  08 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{-j\cdot\omega}\cdot(e^{j\cdot\omega} - e^{-j\cdot\omega})$\\
    1.58        \` trick~!\\
    1.59  09 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{\omega}\cdot(\frac{-e^{j\cdot\omega} + e^{-j\cdot\omega}}{j})$\\
    1.60 @@ -178,18 +196,12 @@
    1.61  }
    1.62  \end{frame}
    1.63  
    1.64 -\begin{frame}\frametitle{Fourier transform expl 2b}
    1.65 -Voraussetzungen
    1.66 -
    1.67 -
    1.68 +\begin{frame}\frametitle{FT expl 2b}
    1.69 +prerequisites
    1.70  \end{frame}
    1.71  
    1.72 -\begin{frame}\frametitle{Fourier transform expl 2b - table}
    1.73 -TODO
    1.74 -\end{frame}
    1.75 -
    1.76 -\section[Convolution]{Convolution}
    1.77 -%\subsection[]{}
    1.78 +\section[Discrete time]{Discrete-time systems}
    1.79 +\subsection[Convolution]{Convolution}
    1.80  \begin{frame}\frametitle{Convolution (Faltung)}
    1.81  TODO
    1.82  \end{frame}
    1.83 @@ -200,6 +212,11 @@
    1.84  TODO
    1.85  \end{frame}
    1.86  
    1.87 +\subsection[]{Indextranformation}
    1.88 +\begin{frame}\frametitle{TODO}
    1.89 +TODO
    1.90 +\end{frame}
    1.91 +
    1.92  \subsection[Inverse ${\cal Z}$]{Inverse ${\cal Z}$ transform}
    1.93  \begin{frame}\frametitle{Development effort}
    1.94  {\small
    1.95 @@ -225,12 +242,6 @@
    1.96  }
    1.97  \end{frame}
    1.98  
    1.99 -\section[]{Indextranformation}
   1.100 -%\subsection[]{}
   1.101 -\begin{frame}\frametitle{TODO}
   1.102 -TODO
   1.103 -\end{frame}
   1.104 -
   1.105  
   1.106  \end{document}
   1.107