1.1 --- a/doc-src/isac/jrocnik/calulations.tex	Mon Feb 20 18:31:00 2012 +0100
     1.2 +++ b/doc-src/isac/jrocnik/calulations.tex	Wed Mar 07 15:29:02 2012 +0100
     1.3 @@ -34,7 +34,7 @@
     1.4     \right.$
     1.5  \end{center}
     1.6  
     1.7 -\textbf{(b)} Now consider the given delayed impulse, determine its fourie transformation and calculate phase and magnitude:
     1.8 +\textbf{\noindent (b)} Now consider the given delayed impulse, determine its fourie transformation and calculate phase and magnitude:
     1.9  
    1.10  \begin{center}
    1.11  $x(t)= \left\{
    1.12 @@ -46,7 +46,7 @@
    1.13  \end{center}
    1.14  
    1.15  \subsubsection{Solution}
    1.16 -\textbf{(a)}
    1.17 +\textbf{(a)} \textsf{Subproblem 1}
    1.18  \onehalfspace{
    1.19  \begin{tabbing}
    1.20  000\=\kill
    1.21 @@ -69,11 +69,10 @@
    1.22  \end{tabbing}
    1.23  }
    1.24  
    1.25 -\textbf{(b)}
    1.26 +\noindent\textbf{(b)} \textsf{Subproblem 1}
    1.27  \onehalfspace{
    1.28  \begin{tabbing}
    1.29  000\=\kill
    1.30 -\textsf{Subproblem 1}\\
    1.31  \texttt{\footnotesize{01}} \> Definition: $X(j\omega)=\int_\infty^\infty{x(t)\cdot e^{-j\omega t}}$\\
    1.32  \`Insert Condition: $x(t) = 1\;$ for $\;\{1\leq t\;\land\;t\leq 3\}\;$ and $\;x(t)=0\;$ otherwise\\
    1.33  \texttt{\footnotesize{02}} \> $X(j\omega)=\int_{-1}^{1}{1\cdot e^{-j\omega t}}$\\
    1.34 @@ -91,7 +90,7 @@
    1.35  \texttt{\footnotesize{08}} \> $\frac{1}{\omega}\cdot e^{j\omega2}\cdot(\frac{e^{j\omega} - e^{-j\omega}}{j})$\\
    1.36        \` table\\
    1.37  \texttt{\footnotesize{09}} \> $2\cdot e^{j\omega2}\cdot\frac{\sin\;\omega}{\omega}$\\
    1.38 -\textsf{Subproblem 2}\\
    1.39 +\noindent\textbf{(b)} \textsf{Subproblem 2}\\
    1.40  \`Definition: $X(j\omega)=|X(j\omega)|\cdot e^{arg(X(j\omega))}$\\
    1.41  \`$|X(j\omega)|$ is called \emph{Magnitude}\\
    1.42  \`$arg(X(j\omega))$ is called \emph{Phase}\\
    1.43 @@ -99,7 +98,6 @@
    1.44  \texttt{\footnotesize{11}} \> $arg(X(j\omega)=-2\omega$\\
    1.45  \end{tabbing}
    1.46  }
    1.47 -
    1.48  %------------------------------------------------------------------------------
    1.49  %CONVOLUTION
    1.50  
    1.51 @@ -152,7 +150,7 @@
    1.52  %------------------------------------------------------------------------------
    1.53  %Z-Transformation
    1.54  
    1.55 -\subsection{$\cal Z$-Transformation\label{sec:calc:ztrans}}
    1.56 +\subsection{Z-Transformation\label{sec:calc:ztrans}}
    1.57  \subsubsection*{Problem\endnote{Problem submitted by Bernhard Geiger. Originally part of the signal processing problem class 5, summer term 2008.}}
    1.58  Determine the inverse $\cal{z}$ transform of the following expression. Hint: applay the partial fraction expansion.
    1.59