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%%
%% This is file `trfexamp.tex',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% trfsigns.dtx (with options: `sample')
%%
%%
%% This file is part of the trfsigns package
%% -----------------------------------------
%%
%% Copyright (C) 1998 Kai Rascher. All rights reserved.
%%
%% To produce the example in the way you like you are allowed
%% to change this file.
%%
%% 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
%%
%% End of file `trfexamp.tex'.
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