diff --git a/ex04/BASK.png b/ex04/BASK.png new file mode 100644 index 0000000..871a8e1 --- /dev/null +++ b/ex04/BASK.png Binary files differ diff --git a/ex04/BFSK.png b/ex04/BFSK.png new file mode 100644 index 0000000..c98975c --- /dev/null +++ b/ex04/BFSK.png Binary files differ diff --git a/ex04/BPSK.png b/ex04/BPSK.png new file mode 100644 index 0000000..78cddea --- /dev/null +++ b/ex04/BPSK.png Binary files differ diff --git a/ex04/Ex-04.pdf b/ex04/Ex-04.pdf new file mode 100644 index 0000000..4e58d5c --- /dev/null +++ b/ex04/Ex-04.pdf Binary files differ diff --git a/ex04/QAM8.png b/ex04/QAM8.png new file mode 100644 index 0000000..4bd6c0d --- /dev/null +++ b/ex04/QAM8.png Binary files differ diff --git a/ex04/kn04.pdf b/ex04/kn04.pdf new file mode 100644 index 0000000..18ba791 --- /dev/null +++ b/ex04/kn04.pdf Binary files differ diff --git a/ex04/kn04.tex b/ex04/kn04.tex new file mode 100644 index 0000000..76a9fd7 --- /dev/null +++ b/ex04/kn04.tex @@ -0,0 +1,154 @@ +\documentclass[a4paper,12pt]{scrartcl} +\usepackage[ngerman]{babel} +\usepackage{graphicx} %BIlder einbinden +\usepackage{amsmath} %erweiterte Mathe-Zeichen +\usepackage{amsfonts} %weitere fonts +\usepackage[utf8]{inputenc} %Umlaute & Co +\usepackage{hyperref} %Links +\usepackage{ifthen} %ifthenelse +\usepackage{enumerate} + +\usepackage{color} +\usepackage{algpseudocode} %Pseudocode +\usepackage{dsfont} % schöne Zahlenräumezeichen +\usepackage{amssymb, amsthm} %noch stärker erweiterte Mathe-Zeichen +\usepackage{tikz} %TikZ ist kein Zeichenprogramm +\usetikzlibrary{trees,automata,arrows,shapes} +\usepackage{pgfplots} + +\pagestyle{empty} + + +\topmargin-50pt + +\newcounter{aufgabe} +\def\tand{&} + +\newcommand{\makeTableLine}[2][0]{% +\setcounter{aufgabe}{1}% +\whiledo{\value{aufgabe} < #1}% +{% +#2\tand\stepcounter{aufgabe}% +} +} + +\newcommand{\aufgTable}[1]{ +\def\spalten{\numexpr #1 + 1 \relax} +\begin{tabular}{|*{\spalten}{p{1cm}|}} +\makeTableLine[\spalten]{A\theaufgabe}$\Sigma$~~\\ \hline +\rule{0pt}{15pt}\makeTableLine[\spalten]{}\\ +\end{tabular} +} + +\def\header#1#2#3#4#5#6#7{\pagestyle{empty} +\begin{minipage}[t]{0.47\textwidth} +\begin{flushleft} +{\bf #4}\\ +#5 +\end{flushleft} +\end{minipage} +\begin{minipage}[t]{0.5\textwidth} +\begin{flushright} +#6 \vspace{0.5cm}\\ +% Number of Columns Definition of Columns second empty line +% \begin{tabular}{|*{5}{C{1cm}|}}\hline A1&A2&A3&A4&$\Sigma$\\\hline&&&&\\\hline\end{tabular}\\\vspace*{0.1cm} +\aufgTable{#7} +\end{flushright} +\end{minipage} +\vspace{1cm} +\begin{center} +{\Large\bf Blatt #1} + +{(Abgabe #3)} +\end{center} +} + + + +%counts the exercisenumber +\newcounter{n} + +%Kommando für Aufgaben +%\Aufgabe{AufgTitel}{Punktezahl} +\newcommand{\Aufgabe}[2]{\stepcounter{n} +\textbf{Aufgabe \arabic{n}: #1} (#2 Punkte)} + +\newcommand{\textcorr}[1]{\textcolor{red}{#1}} +\newenvironment{corr}{\color{red}}{\color{black}\newline} +\newcommand{\ok}{\begin{corr} + $\checkmark$ + \end{corr}} + +\begin{document} +%\header{BlattNr}{Tutor}{Abgabedatum}{Vorlesungsname}{Namen}{Semester}{Anzahl Aufgaben} +\header{4}{}{2015-11-11}{Kommunikationsnetze}{\textit{Jonas Jaszkowic, 3592719}\\\textit{Jan-Peter Hohloch, 3908712}}{WS 15/16}{4} +\vspace{1cm} +\Aufgabe{Scrambling}{5+5+10+10} +\begin{enumerate} + \item To be perfectly in sync, the transmitter and receiver must have access to very accurate and identical time signals. + Due to technical difficulties this is often not the case, so that transmitter and receiver have slightly different time signals. + This results in incorrectly assigned bits, e.g. when the receiver reads a bit short time later than it is supposed to do. + \item Synchronization issues can be fixed by introducing synchronization bits in the signal. Usually the signal must + be chunked into frames, at the beginning of each frame a synchronization bit is added. Subsequent synchronization bits form + a specific binary pattern which repeats at a regular interval in the stream. This is used to identify the current + synchronization state (in sync vs. out of sync). + \item The bit sequence $011000000000100000000110$ is given. + \begin{itemize} + \item[a)] AMI (Alternate Mark Inversion, 0 is encoded as zero, + 1 is alternately encoded as positive or negative voltage): + \begin{align*} + 0+-000000000+00000000-+0 + \end{align*} + B8ZS substitutes eight consecutive zeros with $000VB0VB$: ($+00000000$ is encoded as $+000+-0-+$, $-00000000$ is encoded as $-000-+0+-0$): + \begin{align*} + 0+\mathbf{-000-+0+-0}\mathbf{+000+-0-+} + \end{align*} + \item[b)] HDB3 ($0$ is encoded as $0$, $1$ is alternately encoded as positive or negative voltage, + $0000$ as $000V$, where $V$ is a violation pulse, $0000 0000$ as $B00V B00V$, where $B$ is a balancing pulse): + \begin{align*} + 0+-\mathbf{B00V B00V}0+\mathbf{B00V B00V}-+0 + \end{align*} + \end{itemize} +\end{enumerate} +\Aufgabe{Pulse-Code Modulation}{15+15+5+5} +\begin{enumerate} + \item We have $8$ available levels from $0$ to $7$. The sampling points lead to the level sequence $3,6,0,2,6,4,1,2,3$ and thus to + the word sequence $011,110,000,010,110,100,001,010,011$. + \item The word sequence $011,110,000,010,110,100,001,010,011$ modulated using the given constellation diagram and a sine as the carrier. + The amplitude modulations are $-1, 1, -2, -1, 1, 2, -2, 1$ and $-2$. The phase modulations are $10/8, 2/8, 7/8, 6/8, 2/8, 1/8, 9/8, 6/8$ and $10/8$ of $\pi$. + Two periods of each word are shown: \par + \begin{minipage}{\linewidth} + \centering + \includegraphics[width=\linewidth]{QAM8.png} + \end{minipage} + \item According to the Nyquist theorem, the sampling rate $f_s$ must be at least 2 times the highest frequency contained in the signal. + Thus, a sampling rate of $2 \cdot 4kHz = 8kHz$ is necessary for human voice. + \item The minimum bandwidth for transmission of PCM modulated signals is given as: + \begin{align*} + B_{PCM} = c \cdot 2 \cdot B_{analog} \cdot n_{b} \cdot \frac{1}{r} + \end{align*} + where $c$ is the average probability, that the next bit changes ($c = 0.5$), $r$ is the number of data per signal (here $r = 2$). + Therefore the required bandwidth is: + \begin{align*} + B = 0.5 \cdot 8000Hz \cdot 8bit \cdot \frac{1}{2} = 16kHz + \end{align*} +\end{enumerate} +\Aufgabe{Modulation}{10+10+10} +\begin{enumerate} + \item Binary Amplitude Shift Keying (BASK): \par + \begin{minipage}{\linewidth} + \centering + \includegraphics[width=\linewidth]{BASK.png} + \end{minipage} + \item Binary Frequency Shift Keying (BFSK): \par + \begin{minipage}{\linewidth} + \centering + \includegraphics[width=\linewidth]{BFSK.png} + \end{minipage} + \item Binary Phase Shift Keying (BPSK): \par + \begin{minipage}{\linewidth} + \centering + \includegraphics[width=\linewidth]{BPSK.png} + \end{minipage} +\end{enumerate} +\end{document}