1.1 --- a/doc-src/isac/jrocnik/eJMT-paper/jrocnik_eJMT.tex	Tue Oct 30 21:07:44 2012 +0100
     1.2 +++ b/doc-src/isac/jrocnik/eJMT-paper/jrocnik_eJMT.tex	Wed Oct 31 14:07:00 2012 +0100
     1.3 @@ -246,12 +246,47 @@
     1.4  \end{center}
     1.5  \end{figure}
     1.6  
     1.7 -The problem is from the domain of Signal Processing and requests to
     1.8 -determine the inverse ${\cal z}$-transform for a given term.
     1.9 -Fig.\ref{fig-interactive}
    1.10 -also shows the beginning of the interactive construction of a solution
    1.11 -for the problem. This construction is done in the right window named
    1.12 -``Worksheet''.
    1.13 +\paragraph{The Engineering Background of the Problem} comes out of the domain 
    1.14 +Signal Processing, which takes a major part n the authors field of education. 
    1.15 +The given Problem requests to determine the inverse $z$-transform for a 
    1.16 +given term.
    1.17 +\par
    1.18 +``The $z$-Transform for discrete-time signals is the counterpart of the 
    1.19 +Laplace transform for continuous-time signals, and they each have a similar 
    1.20 +relationship to the corresponding Fourier transform. One motivation for 
    1.21 +introducing this generalization is that the Fourier transform does not 
    1.22 +converge for all sequences, and it is useful to have a generalization of the 
    1.23 +Fourier transform that encompasses a broader class of signals. A second 
    1.24 +advantage is that in analytic problems, the $z$-transform notation is often 
    1.25 +more convenient than the Fourier transform notation.''
    1.26 +~\cite[p. 128]{oppenheim2010discrete}
    1.27 +\par
    1.28 +The $z$-transform can be defined as:
    1.29 +\begin{equation}
    1.30 +X(z)=\sum_{n=-\infty }^{\infty }x[n]z^{-n}
    1.31 +\end{equation}
    1.32 +Upper equation transforms a discrete time sequence $x[n]$ into the function 
    1.33 +$X(z)$ where $z$ is a continuous complex variable. The inverse function (as it 
    1.34 +is used in the given problem) is defined as:
    1.35 +\begin{equation}
    1.36 +x[n]=\frac{1}{2\pi j} \oint_{C} X(z)\cdot z^{n-1} dz
    1.37 +\end{equation}
    1.38 +The letter $C$ represents a contour within the range of converge of the $z$-
    1.39 +transform. The unit circle can be a special case of this contour. Remember 
    1.40 +that $j$ is the complex number in the field of engineering.
    1.41 +As this transformation requires high effort to be solved, tables of 
    1.42 +common transform pairs are used in education as well as in (TODO: real); such 
    1.43 +tables can be found at~\cite{wiki:1} or~\cite[Table~3.1]{oppenheim2010discrete} as well.
    1.44 +A completely solved and more detailed example can be found at
    1.45 +~\cite[p. 149f]{oppenheim2010discrete}. The upcoming implementation tries to 
    1.46 +fit this example in the way it is toughed at the authors university.
    1.47 +
    1.48 +
    1.49 +
    1.50 +\paragraph{The educational aspect} can be explained by having a look at 
    1.51 +Fig.\ref{fig-interactive} which shows the beginning of the interactive 
    1.52 +construction of a solution for the problem. This construction is done in the 
    1.53 +right window named ``Worksheet''.
    1.54  \par
    1.55  User-interaction on the Worksheet is {\em checked} and {\em guided} by
    1.56  TP services:

     2.1 --- a/doc-src/isac/jrocnik/eJMT-paper/references.bib	Tue Oct 30 21:07:44 2012 +0100
     2.2 +++ b/doc-src/isac/jrocnik/eJMT-paper/references.bib	Wed Oct 31 14:07:00 2012 +0100
     2.3 @@ -276,3 +276,11 @@
     2.4    volume = 	 {4},
     2.5    address = 	 {Nomi, Japan}
     2.6  }
     2.7 +
     2.8 +@misc{ wiki:1,
     2.9 +   author = {Wikipedia},
    2.10 +   Title = {Table of common Z-transform pairs},
    2.11 +   year = {2012},
    2.12 +   url = {http://en.wikipedia.org/wiki/Z-transform#Table_of_common_Z-transform_pairs},
    2.13 +   note = {[Online; accessed 31-Oct-2012]}
    2.14 + }
    2.15 \ No newline at end of file