\documentclass[a4paper, 12pt]{article} \usepackage{mathtext} \usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage[russian]{babel} \usepackage{amsmath} \usepackage{titlesec} \usepackage{scrextend} \usepackage{graphicx} \usepackage{tikz} \usetikzlibrary{shapes.misc} \usepackage{pdflscape} \DeclareSymbolFont{T2Aletters}{T2A}{cmr}{m}{it} \graphicspath{ {./images/} } % Установки для отрисовки решеток кодера \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] \tikzstyle{highlight}=[circle,fill=blue,text=white,scale=0.7] \newcounter{ctra} \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 \ifodd\value{ctra} \draw[lightedge] (s#1#2) -- (s\xplusone3); \else \draw[lightedge] (s#1#2) -- (s\xplusone1); \fi } % #1=x; #2=y; #3=In; #4=Out \newcommand{\trellisInOut}[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} \begin{document} \section{Исходные данные} \[ m=41 \] \begin{center} \begin{tabular}{ | p{5cm} | p{5cm} | p{5cm} | } \hline Предельные уровни аналогового сигнала \(a_{min}\), \(a_{max}\) (В) & \(a_{max}=25,6\) В;\newline\(a_{min}=-25,6\) В & Внести свои данные \\ \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 \\ \hline 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 Вид модуляции & КАМ-16 & \\ \hline \end{tabular} \end{center} \section{Аналого-цифровой преобразователь} \[ \Delta t \leq \frac{1}{2f_B}=\frac1 {2\cdot 14100} = 3,546\cdot 10^{-5}\, с \] \[ f_d=\frac{1}{\Delta t}\geq 2f_B=\frac{1}{3,546\cdot 10^{-5}}=28200 \] \[ 377_{10}=101111001_2 \] \[ k=9;\, L=2^9 = 512 \] \section{Кодер} \begin{center} \includegraphics[scale=0.8]{coder} \begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | } \hline Входной сигнал &1&0&1&1&1&1&0&0&1\\ \hline Выходной сигнал &11&10&00&01&10&10&01&11&11\\ \hline \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] {$s_4=11$}; % 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} \foreach \x in {2,...,8} { \foreach \y in {0,...,3} { \trellisEdges{\x}{\y} } } % 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}{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] \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, align=right] {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} Сегмент решетки декодера от $t=0$, до $t=3$. \begin{tikzpicture}[x=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] {$s_4=11$}; % Nodes \foreach \x in {0,...,3} { \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} \foreach \x in {2,...,2} { \foreach \y in {0,...,3} { \trellisEdges{\x}{\y} } } \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 (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] {$\times$}; % Inputs and Outputs \node at (-0.5,4) [left, align=right] {Входная\\пара}; \trellisIn{0}{11} \trellisIn{1}{00} \trellisIn{2}{00} \end{tikzpicture} Сегмент решетки декодера от $t=0$, до $t=4$. \begin{tikzpicture}[x=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] {$s_4=11$}; % Nodes \foreach \x in {0,...,4} { \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} \foreach \x in {2,...,3} { \foreach \y in {0,...,3} { \trellisEdges{\x}{\y} } } \draw[activeedge] (s00) -- (s11); \draw[activeedge] (s11) -- (s22); \draw[activeedge] (s22) -- (s31); \draw[activeedge] (s11) -- (s23); \draw[activeedge] (s23) -- (s32); \draw[activeedge] (s23) -- (s33); \draw[activeedge] (s31) -- (s43); \draw[activeedge] (s32) -- (s41); \draw[activeedge] (s32) -- (s40); \draw[activeedge] (s33) -- (s42); \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 (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] {$\times$}; \node at (1.5,0) [text=red] {$\times$}; \node at (0.5,0) [text=red] {$\times$}; \node at (4,0) [highlight,label=left:{$\frac{1}{1}$}] {$\frac33$}; \node at (4,1) [highlight,label=left:{$\frac{1}{1}$}] {$\frac33$}; \node at (4,2) [highlight,label=left:{$\frac{2}{0}$}] {$\frac32$}; \node at (4,3) [highlight,label=left:{$\frac{0}{2}$}] {$\frac14$}; \node at (3.5,0) [text=red] {$\times$}; \node at (3.5,0.5) [text=red] {$\times$}; \node at (3.5,1.5) [text=red] {$\times$}; \node at (3.5,3) [text=red] {$\times$}; \node at (2.5,0) [text=red] {$\times$}; % Inputs and Outputs \node at (-0.5,4) [left, align=right] {Входная\\пара}; \trellisIn{0}{11} \trellisIn{1}{00} \trellisIn{2}{00} \trellisIn{3}{01} \end{tikzpicture} Сегмент решетки декодера от $t=0$, до $t=5$. \begin{tikzpicture}[x=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] {$s_4=11$}; % Nodes \foreach \x in {0,...,5} { \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} \foreach \x in {2,...,4} { \foreach \y in {0,...,3} { \trellisEdges{\x}{\y} } } \draw[activeedge] (s00) -- (s11); \draw[activeedge] (s11) -- (s22); \draw[activeedge] (s22) -- (s31); \draw[activeedge] (s11) -- (s23); \draw[activeedge] (s23) -- (s32); \draw[activeedge] (s23) -- (s33); \draw[activeedge] (s31) -- (s43); \draw[activeedge] (s32) -- (s41); \draw[activeedge] (s33) -- (s42); \draw[activeedge] (s41) -- (s52); \draw[activeedge] (s42) -- (s50); \draw[activeedge] (s42) -- (s51); \draw[activeedge] (s43) -- (s53); \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 (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] {$\times$}; \node at (1.5,0) [text=red] {$\times$}; \node at (0.5,0) [text=red] {$\times$}; \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 (3.5,0) [text=red] {$\times$}; \node at (3.5,0.5) [text=red] {$\times$}; \node at (3.5,1.5) [text=red] {$\times$}; \node at (3.5,3) [text=red] {$\times$}; \node at (2.5,0) [text=red] {$\times$}; \node at (5,0) [highlight,label=left:{$\frac{1}{1}$}] {$\frac43$}; \node at (5,1) [highlight,label=left:{$\frac{1}{1}$}] {$\frac43$}; \node at (5,2) [highlight,label=left:{$\frac{0}{2}$}] {$\frac33$}; \node at (5,3) [highlight,label=left:{$\frac{2}{0}$}] {$\frac51$}; \node at (4.5,0) [text=red] {$\times$}; \node at (4.5,0.5) [text=red] {$\times$}; \node at (4.5,2.5) [text=red] {$\times$}; \node at (4.5,2) [text=red] {$\times$}; \node at (3.5,1) [text=red] {$\times$}; % Inputs and Outputs \node at (-0.5,4) [left, align=right] {Входная\\пара}; \trellisIn{0}{11} \trellisIn{1}{00} \trellisIn{2}{00} \trellisIn{3}{01} \trellisIn{4}{10} \end{tikzpicture} Сегмент решетки декодера от $t=0$, до $t=6$. \begin{tikzpicture}[x=1.8cm, 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] {$s_4=11$}; % Nodes \foreach \x in {0,...,6} { \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} \foreach \x in {2,...,5} { \foreach \y in {0,...,3} { \trellisEdges{\x}{\y} } } \draw[activeedge] (s00) -- (s11); \draw[activeedge] (s11) -- (s22); \draw[activeedge] (s22) -- (s31); \draw[activeedge] (s11) -- (s23); \draw[activeedge] (s23) -- (s32); \draw[activeedge] (s23) -- (s33); \draw[activeedge] (s31) -- (s43); \draw[activeedge] (s32) -- (s41); \draw[activeedge] (s33) -- (s42); \draw[activeedge] (s41) -- (s52); \draw[activeedge] (s42) -- (s51); \draw[activeedge] (s43) -- (s53); \draw[activeedge] (s51) -- (s62); \draw[activeedge] (s52) -- (s61); \draw[activeedge] (s52) -- (s60); \draw[activeedge] (s53) -- (s63); \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 (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] {$\times$}; \node at (1.5,0) [text=red] {$\times$}; \node at (0.5,0) [text=red] {$\times$}; \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 (3.5,0) [text=red] {$\times$}; \node at (3.5,0.5) [text=red] {$\times$}; \node at (3.5,1.5) [text=red] {$\times$}; \node at (3.5,3) [text=red] {$\times$}; \node at (2.5,0) [text=red] {$\times$}; \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 (4.5,0) [text=red] {$\times$}; \node at (4.5,0.5) [text=red] {$\times$}; \node at (4.5,2.5) [text=red] {$\times$}; \node at (4.5,2) [text=red] {$\times$}; \node at (3.5,1) [text=red] {$\times$}; \node at (6,0) [highlight,label=left:{$\frac{1}{1}$}] {$\frac44$}; \node at (6,1) [highlight,label=left:{$\frac{1}{1}$}] {$\frac44$}; \node at (6,2) [highlight,label=left:{$\frac{0}{2}$}] {$\frac33$}; \node at (6,3) [highlight,label=left:{$\frac{2}{0}$}] {$\frac51$}; \node at (5.5,0) [text=red] {$\times$}; \node at (5.5,0.5) [text=red] {$\times$}; \node at (5.5,2.5) [text=red] {$\times$}; \node at (5.5,2) [text=red] {$\times$}; \node at (4.5,1) [text=red] {$\times$}; % Inputs and Outputs \node at (-0.5,4) [left, align=right] {Входная\\пара}; \trellisIn{0}{11} \trellisIn{1}{00} \trellisIn{2}{00} \trellisIn{3}{01} \trellisIn{4}{10} \trellisIn{5}{10} \end{tikzpicture} \end{document}