diff --git a/ex03/kn03.pdf b/ex03/kn03.pdf index ef489aa..400fcd2 100644 --- a/ex03/kn03.pdf +++ b/ex03/kn03.pdf Binary files differ diff --git a/ex03/kn03.tex b/ex03/kn03.tex index d0d49f1..c4d5cbb 100644 --- a/ex03/kn03.tex +++ b/ex03/kn03.tex @@ -147,5 +147,118 @@ \item $2^1=2$, es kann also jedes Signal ein bit übertragen, da $L=2$. \item Nach Nyquist ist die maximale Bitrate also $2\cdot B=8Mbit/s$ \end{enumerate} +\Aufgabe{Shannon Kapazität}{15} +\begin{align*} + N= & B\cdot \log_2\left(1+SNR\right) &\approx & B\cdot \frac{10}{3}\log_{10} SNR\\ + \Leftrightarrow & 3\log_2\left(1+SNR\right) &\approx & 10\log_{10} SNR\\ + \Leftrightarrow & \underbrace{\frac{3\ln 10}{10\ln 2}}_{\approx 1} \underbrace{\ln\left(1+SNR\right)}_{\approx \ln SNR} &\approx &\ln SNR +\end{align*} \qed\pagebreak\\ +\Aufgabe{Line Codes}{5+15+5+10} + \begin{enumerate} + \item unipolar NRZ: Signal: 101100101000\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=0.7cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,1) (1,0) (2,1) (3,1) (4,0) (5,0) (6,1) (7,0) (8,1) (9,0) (10,0) (11,0) (12,0)}; + \end{axis} + \end{tikzpicture} + \item \begin{itemize} + \item NRZ-I: Signal: 001000110000\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=0.7cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,0) (1,0) (2,1) (3,0) (4,0) (5,0) (6,1) (7,1) (8,0) (9,0) (10,0) (11,0) (12,0)}; + \end{axis} + \end{tikzpicture} + \item Polar RZ: Signal: 1-111-1-11-11-1-1-1\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=1cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,1) (0.5,1) (0.5,0) (1,0) (1,-1) (1.5,-1) (1.5,0) (2,0) (2,1) (2.5,1) (2.5,0) (3,0) (3,1) (3.5,1) (3.5,0) (4,0) (4,-1) (4.5,-1) (4.5,0) (5,0) (5,-1) (5.5,-1) (5.5,0) (6,0) (6,1) (6.5,1) (6.5,0) (7,0) (7,-1) (7.5,-1) (7.5,0) (8,0) (8,1) (8.5,1) (8.5,0) (9,0) (9,-1) (9.5,-1) (9.5,0) (10,0) (10,-1) (10.5,-1) (10.5,0) (11,0) (11,-1) (11.5,-1) (11.5,0) (12,0) + }; + \end{axis} + \end{tikzpicture} + \item Manchester: Signal: uduuddududdd (u=up, d=down)\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=.7cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,-1) (0.5,-1) (0.5,1) (1.5,1) (1.5,-1) (2.5,-1) (2.5,1) (3,1) (3,-1) (3.5,-1) (3.5,1) (4.5,1) (4.5,-1) (5,-1) (5,1) (5.5,1) (5.5,-1) (6.5,-1) (6.5,1) (7.5,1) (7.5,-1) (8.5,-1) (8.5,1) (9.5,1) (9.5,-1) (10,-1) (10,1) (10.5,1) (10.5,-1) (11,-1) (11,1) (11.5,1) (11.5,-1) (12,-1) + }; + \end{axis} + \end{tikzpicture} + \end{itemize} + \item AMI: Signal: 10-1100-101000\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=.7cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,1) (1,0) (2,-1) (3,1) (4,0) (5,0) (6,-1) (7,0) (8,1) (9,0) (10,0) (11,0) (12,0)}; + \end{axis} + \end{tikzpicture} + \item \begin{itemize} + \item PAM-5: Signal: 12-211-2\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=0.7cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,1) (2,2) (4,-2) (6,1) (8,1) (10,-2) (12,-2)}; + \end{axis} + \end{tikzpicture} + \item MLT-3: 110-1-1-1001111\\ + \begin{tikzpicture} + \begin{axis}[ + axis lines = middle, + enlargelimits, + clip=false, + xlabel=t, + ylabel=V, + x=1cm, + y=1cm, + ] + \addplot[thick,mark=none,const plot,red] coordinates { (0,1) (2,0) (3,-1) (6,0) (8,1) (12,1)}; + \end{axis} + \end{tikzpicture} + \end{itemize} + \end{enumerate} \end{document}