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%% trfsigns.dtx  (with options: `sample')
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%% This file is part of the trfsigns package
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%% Copyright (C) 1998 Kai Rascher. All rights reserved.
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%% To produce the example in the way you like you are allowed
%% to change this file.
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%% File: trfsigns.dtx Copyright (C) 1999 Kai Rascher
\documentclass[11pt,a4paper]{article}
\usepackage{german}
\usepackage{trfsigns}

\begin{document}
\noindent
\textbf{\LARGE Transformationszeichen der}

\section*{Laplace-Transformation \protect\laplace, \protect\Laplace}
\begin{eqnarray}
  s(t)        &\laplace& \frac{1}{p}\\[1ex]
  \frac{1}{p} &\Laplace& s(t)
\end{eqnarray}

\section*{(kontinuierlichen) Fourier-Transformation\newline
          \protect\fourier, \protect\Fourier}
\begin{eqnarray}
  \cos(\omega_0 t) &\fourier&
  \pi\left[\delta(\omega-\omega_0) +
           \delta(\omega+\omega_0)\right]\\[1ex]
  \pi\left[\delta(\omega-\omega_0) +
  \delta(\omega+\omega_0)\right] &
  \Fourier&
  \cos(\omega_0 t)
\end{eqnarray}

\section*{diskontinuierlichen Fourier-Transformation\newline
          \protect\dfourier, \protect\Dfourier}
\begin{eqnarray}
  a^n s[n]\quad\mbox{mit~}|a| < 1 &\dfourier&
  \frac{1}{1-a \e^{\im\omega T}}\\[1ex]
  \frac{1}{1-a \e^{\im\omega T}}  &\Dfourier&
  a^n s[n]\quad\mbox{mit~}|a| < 1
\end{eqnarray}

\section*{Z-Transformation
          \protect\ztransf, \protect\Ztransf}
\begin{eqnarray}
  s[n]          &\ztransf& \frac{z}{z-1}\\[1ex]
  \frac{z}{z-1} &\Ztransf& s[n]
\end{eqnarray}

\section*{diskreten Fourier-Transformation
          \protect\dft{}, \protect\DFT{}}
\begin{eqnarray}
  f[n] &\dft{N}&
  F[m] = \sum_{n=0}^{N-1} f[n] \e^{-\im\frac{2 \pi}{N}nm}%
  \:\;(m = 0, 1, \ldots, N-1)\\[1ex]
  F[m] &\DFT{N}&
  f[n] = \frac{1}{N}\sum_{m=0}^{N-1} F[m] \e^{\im\frac{2\pi}{N}mn}%
  \:\;(n = 0, 1, \ldots, N-1)
\end{eqnarray}

\end{document}
\endinput
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