From 80f0472ed40c4b5adc0148c2358a8a72d3e69e96 Mon Sep 17 00:00:00 2001 From: Anatoly Date: Sat, 1 May 2021 04:54:44 +0300 Subject: [PATCH] =?UTF-8?q?=D0=9D=D0=B0=D1=87=D0=B0=D0=BB=20=D1=80=D0=B0?= =?UTF-8?q?=D0=B1=D0=BE=D1=82=D1=83=20=D0=BD=D0=B0=D0=B4=20=D1=80=D0=B5?= =?UTF-8?q?=D1=88=D0=B5=D1=82=D0=BA=D0=B0=D0=BC=D0=B8=20=D0=B4=D0=B5=D0=BA?= =?UTF-8?q?=D0=BE=D0=B4=D0=B5=D1=80=D0=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .gitignore | 2 + term_paper.pdf | Bin 125245 -> 155673 bytes term_paper.tex | 307 +++++++++++++++++++++++++++++++++++++++---------- 3 files changed, 247 insertions(+), 62 deletions(-) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..0e77146 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +*.aux +*.log diff --git a/term_paper.pdf b/term_paper.pdf index 592edd593667bab111544ef043ebef82fcf88c5e..47dbde247c307671453ca0584b51c1e7037a9bf9 100644 GIT binary patch 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\tikzstyle{lightedge}=[dashed] \tikzstyle{mainedge}=[solid] +\tikzstyle{activeedge}=[green, very thick] \tikzstyle{inputBit}=[rectangle,fill=red, text=white] \tikzstyle{outputBit}=[rectangle,fill=blue, text=white] \tikzstyle{pointer}=[orange,->,dashed] \newcounter{ctra} -\newcommand{\trellisEdges}[2]{% +\newcommand{\trellisEdges}[2]{ \setcounter{ctra}{#2} \pgfmathtruncatemacro{\xplusone}{#1 + 1} \ifodd\value{ctra} \draw[mainedge] (s#1#2) -- (s\xplusone2); \else \draw[mainedge] (s#1#2) -- (s\xplusone0); - \fi% + \fi \ifodd\value{ctra} \draw[lightedge] (s#1#2) -- (s\xplusone3); \else \draw[lightedge] (s#1#2) -- (s\xplusone1); - \fi% + \fi } % #1=x; #2=y; #3=In; #4=Out \newcommand{\trellisInOut}[4]{ - \node[inputBit] (in#1) at (#1+0.5,5) {#3}; - \node[outputBit] (out#1) at (#1+0.5,6) {#4}; + \node[inputBit] (in#1) at (#1+0.5,4) {#3}; + \node[outputBit] (out#1) at (#1+0.5,5) {#4}; \draw[pointer] (in#1) -- (#1+0.5,#2); } +% #1=x; #2=y; #3=In +\newcommand{\trellisIn}[2]{ + \node[outputBit] (in#1) at (#1+0.5,4) {#2}; +} + \author{Анатолий Копыл} \title{Курсовая работа} @@ -59,9 +67,9 @@ \hline Верхняя частота спектра аналогового сигнала \(f_В\) & \(f_В =(1+m\cdot 10^{-2})\cdot 10^4\) & \(f_В =14100\) \\ \hline - Заданный уровень квантования & \(j=500-3\cdot m\) & 377 \\ + Заданный уровень квантования & \(j=500-3\cdot m\) & 377 \\ \hline - Спектральная плотность мощности флуктуационной помехи & 41 & \(N_0=2,3\cdot 10^{-7}\, В^2/Гц\)\\ + Спектральная плотность мощности флуктуационной помехи & 41 & \(N_0=2,3\cdot 10^{-7}\, В^2/Гц\)\\ \hline q - номер тактового интервала ошибки & \(q=m\mod{3}+1\) & \(q=3\)\\ \hline @@ -73,8 +81,8 @@ \section{Аналого-цифровой преобразователь} \[ \Delta t \leq \frac{1}{2f_B}=\frac1 {2\cdot 14100} = 3,546\cdot 10^{-5}\, с \] \[ f_d=\frac{1}{\Delta t}\geq 2f_B=\frac{1}{3,546\cdot 10^{-5}}=28200 \] -\[ L=2^9 = 512 \] \[ 377_{10}=101111001_2 \] +\[ k=9;\, L=2^9 = 512 \] \section{Кодер} \begin{center} @@ -89,68 +97,243 @@ \end{tabular} \end{center} +\subsection{Решетка кодера} + \begin{tikzpicture}[x=1.2cm, y=-1cm] - \node at (-0.5,0) [left] {$s_1=00$}; - \node at (-0.5,1) [left] {$s_2=10$}; - \node at (-0.5,2) [left] {$s_3=01$}; - \node at (-0.5,3) [left] {$s_4=11$}; + \node at (-0.5,0) [left] {$s_1=00$}; + \node at (-0.5,1) [left] {$s_2=10$}; + \node at (-0.5,2) [left] {$s_3=01$}; + \node at (-0.5,3) [left] {$s_4=11$}; - % Nodes - \foreach \x in {0,...,9} { - \node at (\x,-.7) {$\x$}; - \foreach \y in {0,...,3} { - \node (s\x\y) at (\x,\y) [circle,fill=blue] {}; - } + % Nodes + \foreach \x in {0,...,9} { + \node at (\x,-.7) {$\x$}; + \foreach \y in {0,...,3} { + \node (s\x\y) at (\x,\y) [circle,fill=black,scale=0.7] {}; } + } - % Edges - \trellisEdges{0}{0} - \trellisEdges{1}{0} - \trellisEdges{1}{1} - \trellisEdges{2}{0} - \trellisEdges{2}{1} - \trellisEdges{2}{2} - \trellisEdges{2}{3} - \trellisEdges{3}{0} - \trellisEdges{3}{1} - \trellisEdges{3}{2} - \trellisEdges{3}{3} - \trellisEdges{4}{0} - \trellisEdges{4}{1} - \trellisEdges{4}{2} - \trellisEdges{4}{3} - \trellisEdges{5}{0} - \trellisEdges{5}{1} - \trellisEdges{5}{2} - \trellisEdges{5}{3} - \trellisEdges{6}{0} - \trellisEdges{6}{1} - \trellisEdges{6}{2} - \trellisEdges{6}{3} - \trellisEdges{7}{0} - \trellisEdges{7}{1} - \trellisEdges{7}{2} - \trellisEdges{7}{3} - \trellisEdges{8}{0} - \trellisEdges{8}{1} - \trellisEdges{8}{2} - \trellisEdges{8}{3} + % Edges + \trellisEdges{0}{0} + \trellisEdges{1}{0} + \trellisEdges{1}{1} + \foreach \x in {2,...,8} { + \foreach \y in {0,...,3} { + \trellisEdges{\x}{\y} + } + } - % Inputs and Outputs - \node at (-0,5) [left] {Входной бит}; - \node at (-0,6) [left] {Выходной бит}; + % Inputs and Outputs + \node at (-0.5,4) [left] {Входной бит}; + \node at (-0.5,5) [left] {Результат}; - \trellisInOut{0}{0.5}{1}{11} - \trellisInOut{1}{1.5}{0}{10} - \trellisInOut{2}{1.5}{1}{00} - \trellisInOut{3}{2}{1}{01} - \trellisInOut{4}{3}{1}{10} - \trellisInOut{5}{3}{1}{10} - \trellisInOut{6}{2.5}{1}{01} - \trellisInOut{7}{1}{0}{11} - \trellisInOut{8}{0}{1}{11} + \trellisInOut{0}{0.5}{1}{11} + \trellisInOut{1}{1.5}{0}{10} + \trellisInOut{2}{1.5}{1}{00} + \trellisInOut{3}{2}{1}{01} + \trellisInOut{4}{3}{1}{10} + \trellisInOut{5}{3}{1}{10} + \trellisInOut{6}{2.5}{0}{01} + \trellisInOut{7}{1}{0}{11} + \trellisInOut{8}{0.5}{1}{11} \end{tikzpicture} +Длительность двоичного символа \(T_В\) на выходе кодера: +\[T_В=\frac{\Delta t}{2k}=\frac{3,546\cdot 10^{-5}}{2\cdot 9}= +1,97\cdot 10^{-6}\,с\] +\section{Декодер} +По каналу передавался код \(\overline{u}=11 10 00 01 10 10 01 11 11\). +Ошибка произошла на тактовом интервале \(q=3\). +Таким образом, на вход декодера поступает последовательность +\(\overline{Z}=11 \dot{0}0 00 01 10 10 01 11 11\). Точкой обозначен ошибочно принятый символ. + +\subsection{Диаграмма декодера} + +\begin{tikzpicture}[x=1.2cm, y=-1cm, + highlight/.style={circle,fill=blue,text=white,scale=0.7} + ] + + \node at (-0.5,0) [left] {$s_1=00$}; + \node at (-0.5,1) [left] {$s_2=10$}; + \node at (-0.5,2) [left] {$s_3=01$}; + \node at (-0.5,3) [left] {$s_4=11$}; + + % Nodes + \foreach \x in {0,...,9} { + \node at (\x,-.7) {$\x$}; + \foreach \y in {0,...,3} { + \node (s\x\y) at (\x,\y) [circle,fill=black,scale=0.7] {}; + } + } + + \node at (0,0) [highlight] {}; + \node at (1,0) [highlight,label=left:{$2$}] {}; + \node at (1,1) [highlight,label=left:{$0$}] {}; + + \node at (2,0) [highlight,label=left:{$0$}] {}; + \node at (2,1) [highlight,label=left:{$2$}] {}; + \node at (2,2) [highlight,label=left:{$1$}] {}; + \node at (2,3) [highlight,label=left:{$1$}] {}; + + \node at (3,0) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (3,1) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (3,2) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (3,3) [highlight,label=left:{$\frac{1}{1}$}] {}; + + \node at (4,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (4,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (4,2) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (4,3) [highlight,label=left:{$\frac{0}{2}$}] {}; + + \node at (5,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (5,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (5,2) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (5,3) [highlight,label=left:{$\frac{2}{0}$}] {}; + + \node at (6,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (6,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (6,2) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (6,3) [highlight,label=left:{$\frac{2}{0}$}] {}; + + \node at (7,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (7,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (7,2) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (7,3) [highlight,label=left:{$\frac{0}{2}$}] {}; + + \node at (8,0) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (8,1) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (8,2) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (8,3) [highlight,label=left:{$\frac{1}{1}$}] {}; + + \node at (9,0) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (9,1) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (9,2) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (9,3) [highlight,label=left:{$\frac{1}{1}$}] {}; + + % Edges + \trellisEdges{0}{0} + \trellisEdges{1}{0} + \trellisEdges{1}{1} + \foreach \x in {2,...,8} { + \foreach \y in {0,...,3} { + \trellisEdges{\x}{\y} + } + } + + % Inputs + \node at (-0.5,4) [left] {Входная пара}; + + \trellisIn{0}{11} + \trellisIn{1}{00} + \trellisIn{2}{00} + \trellisIn{3}{01} + \trellisIn{4}{10} + \trellisIn{5}{10} + \trellisIn{6}{01} + \trellisIn{7}{11} + \trellisIn{8}{11} +\end{tikzpicture} + +\begin{tikzpicture}[x=1.2cm, y=-1cm, + highlight/.style={circle,fill=blue,text=white,scale=0.7} + ] + + \node at (-0.5,0) [left] {$s_1=00$}; + \node at (-0.5,1) [left] {$s_2=10$}; + \node at (-0.5,2) [left] {$s_3=01$}; + \node at (-0.5,3) [left] {$s_4=11$}; + + % Edges + \trellisEdges{0}{0} + \trellisEdges{1}{0} + \trellisEdges{1}{1} + \foreach \x in {2,...,8} { + \foreach \y in {0,...,3} { + \trellisEdges{\x}{\y} + } + } + + % Nodes + \foreach \x in {0,...,9} { + \node at (\x,-.7) {$\x$}; + \foreach \y in {0,...,3} { + \node (s\x\y) at (\x,\y) [circle,fill=black,scale=0.7] {}; + } + } + + \node at (0,0) [highlight] {}; + \node at (1,0) [highlight,label=left:{$2$}] {}; + \node at (1,1) [highlight,label=left:{$0$}] {}; + + \node at (2,0) [highlight,label=left:{$0$}] {}; + \node at (2,1) [highlight,label=left:{$2$}] {}; + \node at (2,2) [highlight,label=left:{$1$}] {}; + \node at (2,3) [highlight,label=left:{$1$}] {}; + + \node at (3,0) [highlight,label=left:{$\frac{0}{2}$}] {$\frac23$}; + \node at (3,1) [highlight,label=left:{$\frac{2}{0}$}] {$\frac41$}; + \node at (3,2) [highlight,label=left:{$\frac{1}{1}$}] {$\frac52$}; + \node at (3,3) [highlight,label=left:{$\frac{1}{1}$}] {$\frac52$}; + + \node at (2.5,1) [text=red] {$\times$}; + \node at (2.5,0.5) [text=red] {$\times$}; + \node at (2.5,1.5) [text=red] {$\times$}; + \node at (2.5,2) [text=red] {$\times$}; + \node at (1.5,0.5) [text=red] {$\times$}; + + \draw[activeedge] (s00) -- (s10); + \draw[activeedge] (s00) -- (s11); + \draw[activeedge] (s10) -- (s20); + \draw[activeedge] (s11) -- (s22); + \draw[activeedge] (s20) -- (s30); + \draw[activeedge] (s22) -- (s31); + \draw[activeedge] (s11) -- (s23); + \draw[activeedge] (s23) -- (s32); + \draw[activeedge] (s23) -- (s33); + + \node at (4,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (4,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (4,2) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (4,3) [highlight,label=left:{$\frac{0}{2}$}] {}; + + \node at (5,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (5,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (5,2) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (5,3) [highlight,label=left:{$\frac{2}{0}$}] {}; + + \node at (6,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (6,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (6,2) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (6,3) [highlight,label=left:{$\frac{2}{0}$}] {}; + + \node at (7,0) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (7,1) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (7,2) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (7,3) [highlight,label=left:{$\frac{0}{2}$}] {}; + + \node at (8,0) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (8,1) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (8,2) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (8,3) [highlight,label=left:{$\frac{1}{1}$}] {}; + + \node at (9,0) [highlight,label=left:{$\frac{2}{0}$}] {}; + \node at (9,1) [highlight,label=left:{$\frac{0}{2}$}] {}; + \node at (9,2) [highlight,label=left:{$\frac{1}{1}$}] {}; + \node at (9,3) [highlight,label=left:{$\frac{1}{1}$}] {}; + + % Inputs and Outputs + \node at (-0.5,4) [left] {Входная пара}; + + \trellisIn{0}{11} + \trellisIn{1}{00} + \trellisIn{2}{00} + \trellisIn{3}{01} + \trellisIn{4}{10} + \trellisIn{5}{10} + \trellisIn{6}{01} + \trellisIn{7}{11} + \trellisIn{8}{11} +\end{tikzpicture} \end{document}