% $Header: /cvsroot/latex-beamer/latex-beamer/solutions/conference-talks/conference-ornate-20min.en.tex,v 1.7 2007/01/28 20:48:23 tantau Exp $

 \documentclass{beamer}

 % This file is a solution template for:

 % - Talk at a conference/colloquium.

 % - Talk length is about 20min.

 % - Style is ornate.

 % Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.

 %

 % In principle, this file can be redistributed and/or modified under

 % the terms of the GNU Public License, version 2.

 %

 % However, this file is supposed to be a template to be modified

 % for your own needs. For this reason, if you use this file as a

 % template and not specifically distribute it as part of a another

 % package/program, I grant the extra permission to freely copy and

 % modify this file as you see fit and even to delete this copyright

 % notice.

 \mode<presentation>

 {

   \usetheme{Hannover}

   % or ...

   \setbeamercovered{transparent}

   % or whatever (possibly just delete it)

 }

 %\usepackage{setspace} %for "\begin{onehalfspace}"

 \usepackage[english]{babel}

 % or whatever

 \usepackage[utf8]{inputenc}

 % or whatever

 \usepackage{times}

 \usepackage[T1]{fontenc}

 % Or whatever. Note that the encoding and the font should match. If T1

 % does not look nice, try deleting the line with the fontenc.

 \def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}

 \def\sisac{{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}}

 \title[TODO] % (optional, use only with long paper titles)

 {TODO}

 \subtitle{TODO}

 \author[Rocnik] % (optional, use only with lots of authors)

 {Jan~Rocnik}

 % - Give the names in the same order as the appear in the paper.

 % - Use the \inst{?} command only if the authors have different

 %   affiliation.

 \institute % (optional, but mostly needed)

 {

   Technische Universit\"at Graz\\

   Institut f\"ur TODO

 }

 % - Use the \inst command only if there are several affiliations.

 % - Keep it simple, no one is interested in your street address.

 % \date[CFP 2003] % (optional, should be abbreviation of conference name)

 % {Conference on Fabulous Presentations, 2003}

 % - Either use conference name or its abbreviation.

 % - Not really informative to the audience, more for people (including

 %   yourself) who are reading the slides online

 % \subject{Theoretical Computer Science}

 % This is only inserted into the PDF information catalog. Can be left

 % out.

 % If you have a file called "university-logo-filename.xxx", where xxx

 % is a graphic format that can be processed by latex or pdflatex,

 % resp., then you can add a logo as follows:

 % \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}

 % \logo{\pgfuseimage{university-logo}}

 % Delete this, if you do not want the table of contents to pop up at

 % the beginning of each subsection:

 \AtBeginSubsection[]

 {

   \begin{frame}<beamer>{Outline}

     \tableofcontents[currentsection,currentsubsection]

   \end{frame}

 }

 % If you wish to uncover everything in a step-wise fashion, uncomment

 % the following command:

 %\beamerdefaultoverlayspecification{<+->}

 \begin{document}

 \begin{frame}

   \titlepage

 \end{frame}

 \begin{frame}{Outline}

   \tableofcontents

   % You might wish to add the option [pausesections]

 \end{frame}

 % Structuring a talk is a difficult task and the following structure

 % may not be suitable. Here are some rules that apply for this

 % solution:

 % - Exactly two or three sections (other than the summary).

 % - At *most* three subsections per section.

 % - Talk about 30s to 2min per frame. So there should be between about

 %   15 and 30 frames, all told.

 % - A conference audience is likely to know very little of what you

 %   are going to talk about. So *simplify*!

 % - In a 20min talk, getting the main ideas across is hard

 %   enough. Leave out details, even if it means being less precise than

 %   you think necessary.

 % - If you omit details that are vital to the proof/implementation,

 %   just say so once. Everybody will be happy with that.

 \section[Fourier]{Fourier transform}

 \subsection[Series]{Fourier series}

 \begin{frame}\frametitle{TODO}

 TODO

 \end{frame}

 \subsection[Transform]{Fourier transform}

 \begin{frame}\frametitle{FT expl 1}

 TODO

 \end{frame}

 \begin{frame}\frametitle{FT expl 2a}

 TODO

 \end{frame}

 \begin{frame}\frametitle{FT expl 2b}

 Problem (from Bernhard)

 \end{frame}

 \begin{frame}\frametitle{FT expl 2b: specification }

 {\footnotesize\it

 fourier transform

 \begin{tabbing}

 1\=postcond \=: \= \= $\;\;\;\;$\=\kill

 \>given    \>:\>  piecewise\_function \\

 \>         \> \>  \>$(x (t::real), [(0,-\infty<t<1), (1,1\leq t\leq 3), (0, 3<t<\infty)])$\\

                         %?(iterativer) datentyp in Isabelle/HOL

 \>         \> \>  translation $T=2$\\

 \>precond  \>:\>  TODO\\

 \>find     \>:\>  $X(j\cdot\omega)$\\

 \>postcond \>:\>  TODO\\

 \end{tabbing}

 }

 \end{frame}

 \begin{frame}\frametitle{FT expl 2b: calculation}

 \footnotesize{

 \begin{tabbing}

 000\=\kill

 01 \> ${\cal F}\;(x(t-2)) =$\\

       \`${\cal F}\;(x(t-T)) = e^{-j\cdot\omega\cdot T}\cdot X\;j\cdot\omega$\\

 02 \> $e^{-j\cdot\omega\cdot 2}\cdot X\;(j\cdot\omega)$\\

       \`definition $X\;(j\cdot\omega)$\\

 03 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-\infty}^\infty x\;t\;\cdot e^{-j\cdot\omega\cdot t} d t$\\

       \` $x\;t = 1\;{\it for}\;\{x.\;-1\leq t\;\land\;t\leq 1\}\;{\it and}\;x\;t=0\;{\it otherwise}$\\

 04 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-1}^1 1\cdot e^{-j\cdot\omega\cdot t} d t$\\

       \` $\int_a^b f\;t\;dt = \int f\;t\;dt\;|_a^b$\\

 05 \> $e^{-j\cdot\omega\cdot 2}\cdot \int 1\cdot e^{-j\cdot\omega\cdot t} d t\;|_{-1}^1$\\

       %\` $\int e^{a\cdot t} = \frac{1}{a}\cdot e^{a\cdot t}$\\

        \` pbl: integration in $\cal C$\\

 06 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot t} \;|_{-1}^1)$\\

       \` $f\;t\;|_a^b = f\;b-f\;a$\\

 07 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot 1} -  \frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot -1})$\\

 \vdots\` pbl: simplification+factorization in $\cal C$\\

 08 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{-j\cdot\omega}\cdot(e^{j\cdot\omega} - e^{-j\cdot\omega})$\\

       \` trick~!\\

 09 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{\omega}\cdot(\frac{-e^{j\cdot\omega} + e^{-j\cdot\omega}}{j})$\\

       \` table\\

 10 \> $e^{-j\cdot\omega\cdot 2}\cdot 2\cdot\frac{\sin\;\omega}{\omega}$

 \end{tabbing}

 }

 \end{frame}

 \begin{frame}\frametitle{FT expl 2b}

 prerequisites

 \end{frame}

 \section[Discrete time]{Discrete-time systems}

 \subsection[Convolution]{Convolution}

 \begin{frame}\frametitle{Convolution (Faltung)}

 TODO

 \end{frame}

 \section[${\cal Z}$ transform]{${\cal Z}$ transform}

 %\subsection[]{}

 \begin{frame}\frametitle{TODO}

 TODO

 \end{frame}

 \subsection[]{Indextranformation}

 \begin{frame}\frametitle{TODO}

 TODO

 \end{frame}

 \subsection[Inverse ${\cal Z}$]{Inverse ${\cal Z}$ transform}

 \begin{frame}\frametitle{Development effort}

 {\small

 \begin{center}

 \begin{tabular}{l|l|r}

 requirements            & comments             &effort\\ \hline\hline

 solve for part.fract.   & \sisac: degree 2     &     0\\

                         & complex nomminators  &    30\\

                         & degree > 2           &    MT\\ \hline

 simplify polynomial     & \sisac               &     0\\

 simplify rational       & \sisac               &     0\\ \hline

 part.fract.decomposition& degree 2             &      \\

                         & specification, method&    30\\ \hline

 ${\cal Z}^{-1}$ table    &                       &   20\\

                         & explanations, figures&    20\\ \hline

 example collection      & with explanations    &    20\\ \hline\hline

                         &                      & 90-120\\

 %                        &                      & 1 MT

 \end{tabular}

 \end{center}

 effort --- in 45min units\\

 MT --- thesis ``factorization'' (mathematics)

 }

 \end{frame}

 \end{document}