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% $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 $
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\documentclass{beamer}
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% This file is a solution template for:
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% - Talk at a conference/colloquium.
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% - Talk length is about 20min.
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% - Style is ornate.
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% Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
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%
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% In principle, this file can be redistributed and/or modified under
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% the terms of the GNU Public License, version 2.
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%
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% However, this file is supposed to be a template to be modified
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% for your own needs. For this reason, if you use this file as a
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% template and not specifically distribute it as part of a another
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% package/program, I grant the extra permission to freely copy and
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% modify this file as you see fit and even to delete this copyright
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% notice.
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\mode<presentation>
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{
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\usetheme{Hannover}
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% or ...
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\setbeamercovered{transparent}
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% or whatever (possibly just delete it)
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}
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%\usepackage{setspace} %for "\begin{onehalfspace}"
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\usepackage[english]{babel}
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% or whatever
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\usepackage[utf8]{inputenc}
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% or whatever
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\usepackage{times}
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\usepackage[T1]{fontenc}
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% Or whatever. Note that the encoding and the font should match. If T1
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% does not look nice, try deleting the line with the fontenc.
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\def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
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\def\sisac{{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}}
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\title[TODO] % (optional, use only with long paper titles)
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{TODO}
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\subtitle{TODO}
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\author[Rocnik] % (optional, use only with lots of authors)
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{Jan~Rocnik}
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% - Give the names in the same order as the appear in the paper.
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% - Use the \inst{?} command only if the authors have different
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% affiliation.
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\institute % (optional, but mostly needed)
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{
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Technische Universit\"at Graz\\
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Institut f\"ur TODO
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}
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% - Use the \inst command only if there are several affiliations.
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% - Keep it simple, no one is interested in your street address.
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% \date[CFP 2003] % (optional, should be abbreviation of conference name)
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% {Conference on Fabulous Presentations, 2003}
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% - Either use conference name or its abbreviation.
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% - Not really informative to the audience, more for people (including
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% yourself) who are reading the slides online
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% \subject{Theoretical Computer Science}
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% This is only inserted into the PDF information catalog. Can be left
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% out.
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% If you have a file called "university-logo-filename.xxx", where xxx
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% is a graphic format that can be processed by latex or pdflatex,
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% resp., then you can add a logo as follows:
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% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
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% \logo{\pgfuseimage{university-logo}}
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% Delete this, if you do not want the table of contents to pop up at
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% the beginning of each subsection:
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\AtBeginSubsection[]
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{
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\begin{frame}<beamer>{Outline}
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\tableofcontents[currentsection,currentsubsection]
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\end{frame}
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}
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% If you wish to uncover everything in a step-wise fashion, uncomment
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% the following command:
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%\beamerdefaultoverlayspecification{<+->}
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\begin{document}
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\begin{frame}
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\titlepage
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\end{frame}
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\begin{frame}{Outline}
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\tableofcontents
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% You might wish to add the option [pausesections]
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\end{frame}
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% Structuring a talk is a difficult task and the following structure
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% may not be suitable. Here are some rules that apply for this
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% solution:
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% - Exactly two or three sections (other than the summary).
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% - At *most* three subsections per section.
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% - Talk about 30s to 2min per frame. So there should be between about
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% 15 and 30 frames, all told.
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% - A conference audience is likely to know very little of what you
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% are going to talk about. So *simplify*!
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% - In a 20min talk, getting the main ideas across is hard
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% enough. Leave out details, even if it means being less precise than
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% you think necessary.
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% - If you omit details that are vital to the proof/implementation,
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% just say so once. Everybody will be happy with that.
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\section[Fourier]{Fourier transform}
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\subsection[Series]{Fourier series}
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\begin{frame}\frametitle{TODO}
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TODO
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\end{frame}
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\subsection[Transform]{Fourier transform}
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\begin{frame}\frametitle{FT expl 1}
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TODO
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\end{frame}
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\begin{frame}\frametitle{FT expl 2a}
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TODO
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\end{frame}
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\begin{frame}\frametitle{FT expl 2b}
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Problem (from Bernhard)
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\end{frame}
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\begin{frame}\frametitle{FT expl 2b: specification }
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{\footnotesize\it
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fourier transform
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\begin{tabbing}
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1\=postcond \=: \= \= $\;\;\;\;$\=\kill
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\>given \>:\> piecewise\_function \\
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\> \> \> \>$(x (t::real), [(0,-\infty<t<1), (1,1\leq t\leq 3), (0, 3<t<\infty)])$\\
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%?(iterativer) datentyp in Isabelle/HOL
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\> \> \> translation $T=2$\\
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\>precond \>:\> TODO\\
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\>find \>:\> $X(j\cdot\omega)$\\
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\>postcond \>:\> TODO\\
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\end{tabbing}
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}
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\end{frame}
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\begin{frame}\frametitle{FT expl 2b: calculation}
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\footnotesize{
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\begin{tabbing}
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000\=\kill
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01 \> ${\cal F}\;(x(t-2)) =$\\
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\`${\cal F}\;(x(t-T)) = e^{-j\cdot\omega\cdot T}\cdot X\;j\cdot\omega$\\
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02 \> $e^{-j\cdot\omega\cdot 2}\cdot X\;(j\cdot\omega)$\\
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\`definition $X\;(j\cdot\omega)$\\
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03 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-\infty}^\infty x\;t\;\cdot e^{-j\cdot\omega\cdot t} d t$\\
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\` $x\;t = 1\;{\it for}\;\{x.\;-1\leq t\;\land\;t\leq 1\}\;{\it and}\;x\;t=0\;{\it otherwise}$\\
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04 \> $e^{-j\cdot\omega\cdot 2}\cdot \int_{-1}^1 1\cdot e^{-j\cdot\omega\cdot t} d t$\\
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\` $\int_a^b f\;t\;dt = \int f\;t\;dt\;|_a^b$\\
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05 \> $e^{-j\cdot\omega\cdot 2}\cdot \int 1\cdot e^{-j\cdot\omega\cdot t} d t\;|_{-1}^1$\\
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%\` $\int e^{a\cdot t} = \frac{1}{a}\cdot e^{a\cdot t}$\\
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\` pbl: integration in $\cal C$\\
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06 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot t} \;|_{-1}^1)$\\
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\` $f\;t\;|_a^b = f\;b-f\;a$\\
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07 \> $e^{-j\cdot\omega\cdot 2}\cdot (\frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot 1} - \frac{1}{-j\cdot\omega}\cdot e^{-j\cdot\omega\cdot -1})$\\
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\vdots\` pbl: simplification+factorization in $\cal C$\\
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08 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{-j\cdot\omega}\cdot(e^{j\cdot\omega} - e^{-j\cdot\omega})$\\
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\` trick~!\\
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09 \> $e^{-j\cdot\omega\cdot 2}\cdot \frac{1}{\omega}\cdot(\frac{-e^{j\cdot\omega} + e^{-j\cdot\omega}}{j})$\\
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\` table\\
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10 \> $e^{-j\cdot\omega\cdot 2}\cdot 2\cdot\frac{\sin\;\omega}{\omega}$
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\end{tabbing}
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}
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\end{frame}
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\begin{frame}\frametitle{FT expl 2b}
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prerequisites
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\end{frame}
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\section[Discrete time]{Discrete-time systems}
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\subsection[Convolution]{Convolution}
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\begin{frame}\frametitle{Convolution (Faltung)}
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TODO
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\end{frame}
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\section[${\cal Z}$ transform]{${\cal Z}$ transform}
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%\subsection[]{}
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\begin{frame}\frametitle{TODO}
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TODO
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\end{frame}
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\subsection[]{Indextranformation}
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\begin{frame}\frametitle{TODO}
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TODO
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\end{frame}
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\subsection[Inverse ${\cal Z}$]{Inverse ${\cal Z}$ transform}
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\begin{frame}\frametitle{Development effort}
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{\small
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\begin{center}
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\begin{tabular}{l|l|r}
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requirements & comments &effort\\ \hline\hline
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solve for part.fract. & \sisac: degree 2 & 0\\
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& complex nomminators & 30\\
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& degree > 2 & MT\\ \hline
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simplify polynomial & \sisac & 0\\
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simplify rational & \sisac & 0\\ \hline
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part.fract.decomposition& degree 2 & \\
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& specification, method& 30\\ \hline
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${\cal Z}^{-1}$ table & & 20\\
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& explanations, figures& 20\\ \hline
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example collection & with explanations & 20\\ \hline\hline
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& & 90-120\\
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% & & 1 MT
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\end{tabular}
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\end{center}
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effort --- in 45min units\\
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MT --- thesis ``factorization'' (mathematics)
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}
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\end{frame}
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\end{document}
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