anatolykopyl/term-paper-tes
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term-paper-tes/term_paper.tex

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\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]
\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,
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}
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