mirror of
https://github.com/anatolykopyl/term-paper-tes.git
synced 2026-03-26 12:54:38 +00:00
Доделал источник сообщения
This commit is contained in:
@@ -1,4 +1,4 @@
|
||||
input_code = {1, 0, 1, 1, 1, 1, 0, 0, 1}
|
||||
input_code = {1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0}
|
||||
|
||||
-- Logical sum
|
||||
function m2s(a, b)
|
||||
@@ -28,6 +28,10 @@ function coder(input_code)
|
||||
return result, states
|
||||
end
|
||||
|
||||
function decoder(input_code)
|
||||
|
||||
end
|
||||
|
||||
result, states = coder(input_code)
|
||||
|
||||
for _, v in ipairs(states) do print(v..' ') end
|
||||
|
||||
681
decoder.tex
681
decoder.tex
@@ -1,4 +1,5 @@
|
||||
\begin{tikzpicture}[x=1.2cm, y=-1cm]
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=1.2cm, y=-1cm]
|
||||
|
||||
\node at (-0.5,0) [left] {$s_1=00$};
|
||||
\node at (-0.5,1) [left] {$s_2=10$};
|
||||
@@ -79,11 +80,13 @@
|
||||
\trellisIn{6}{01}
|
||||
\trellisIn{7}{11}
|
||||
\trellisIn{8}{11}
|
||||
\end{tikzpicture}
|
||||
\end{tikzpicture}
|
||||
|
||||
Сегмент решетки декодера от $t=0$, до $t=3$.
|
||||
\caption{Решетка декодера} \label{fig:decoder}
|
||||
\end{figure}
|
||||
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
|
||||
\node at (-0.5,0) [left] {$s_1=00$};
|
||||
\node at (-0.5,1) [left] {$s_2=10$};
|
||||
@@ -144,11 +147,13 @@
|
||||
\trellisIn{0}{11}
|
||||
\trellisIn{1}{00}
|
||||
\trellisIn{2}{00}
|
||||
\end{tikzpicture}
|
||||
\end{tikzpicture}
|
||||
|
||||
Сегмент решетки декодера от $t=0$, до $t=4$.
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=3$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
|
||||
\node at (-0.5,0) [left] {$s_1=00$};
|
||||
\node at (-0.5,1) [left] {$s_2=10$};
|
||||
@@ -226,11 +231,13 @@
|
||||
\trellisIn{1}{00}
|
||||
\trellisIn{2}{00}
|
||||
\trellisIn{3}{01}
|
||||
\end{tikzpicture}
|
||||
\end{tikzpicture}
|
||||
|
||||
Сегмент решетки декодера от $t=0$, до $t=5$.
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=4$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=2cm, y=-1cm]
|
||||
|
||||
\node at (-0.5,0) [left] {$s_1=00$};
|
||||
\node at (-0.5,1) [left] {$s_2=10$};
|
||||
@@ -324,11 +331,13 @@
|
||||
\trellisIn{2}{00}
|
||||
\trellisIn{3}{01}
|
||||
\trellisIn{4}{10}
|
||||
\end{tikzpicture}
|
||||
\end{tikzpicture}
|
||||
|
||||
Сегмент решетки декодера от $t=0$, до $t=6$.
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=5$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{tikzpicture}[x=1.8cm, y=-1cm]
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=1.8cm, y=-1cm]
|
||||
|
||||
\node at (-0.5,0) [left] {$s_1=00$};
|
||||
\node at (-0.5,1) [left] {$s_2=10$};
|
||||
@@ -438,4 +447,648 @@
|
||||
\trellisIn{3}{01}
|
||||
\trellisIn{4}{10}
|
||||
\trellisIn{5}{10}
|
||||
\end{tikzpicture}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=6$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=1.58cm, 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,...,7} {
|
||||
\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,...,6} {
|
||||
\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) -- (s33);
|
||||
|
||||
\draw[activeedge] (s31) -- (s43);
|
||||
\draw[activeedge] (s33) -- (s42);
|
||||
|
||||
\draw[activeedge] (s42) -- (s51);
|
||||
\draw[activeedge] (s43) -- (s53);
|
||||
|
||||
\draw[activeedge] (s51) -- (s62);
|
||||
\draw[activeedge] (s53) -- (s63);
|
||||
|
||||
\draw[activeedge] (s62) -- (s70);
|
||||
\draw[activeedge] (s62) -- (s71);
|
||||
\draw[activeedge] (s63) -- (s72);
|
||||
\draw[activeedge] (s63) -- (s73);
|
||||
|
||||
\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:{$\frac{1}{1}$}] {};
|
||||
\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 (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] {$\times$};
|
||||
|
||||
\node at (7,0) [highlight,label=left:{$\frac{1}{1}$}] {$\frac54$};
|
||||
\node at (7,1) [highlight,label=left:{$\frac{1}{1}$}] {$\frac54$};
|
||||
\node at (7,2) [highlight,label=left:{$\frac{2}{0}$}] {$\frac61$};
|
||||
\node at (7,3) [highlight,label=left:{$\frac{0}{2}$}] {$\frac43$};
|
||||
|
||||
\node at (6.5,0) [text=red] {$\times$};
|
||||
\node at (6.5,0.5) [text=red] {$\times$};
|
||||
\node at (6.5,1.5) [text=red] {$\times$};
|
||||
\node at (6.5,2) [text=red] {$\times$};
|
||||
\node at (5.5,1) [text=red] {$\times$};
|
||||
\node at (5.5,1.5) [text=red] {$\times$};
|
||||
\node at (4.5,1.5) [text=red] {$\times$};
|
||||
\node at (2.5,2.5) [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}
|
||||
\trellisIn{3}{01}
|
||||
\trellisIn{4}{10}
|
||||
\trellisIn{5}{10}
|
||||
\trellisIn{6}{01}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=7$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=1.36cm, 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,...,8} {
|
||||
\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,...,7} {
|
||||
\foreach \y in {0,...,3} {
|
||||
\trellisEdges{\x}{\y}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
\draw[activeedge] (s00) -- (s11);
|
||||
\draw[activeedge] (s11) -- (s22);
|
||||
\draw[activeedge] (s22) -- (s31);
|
||||
|
||||
\draw[activeedge] (s31) -- (s43);
|
||||
|
||||
\draw[activeedge] (s43) -- (s53);
|
||||
|
||||
\draw[activeedge] (s53) -- (s63);
|
||||
|
||||
\draw[activeedge] (s63) -- (s72);
|
||||
\draw[activeedge] (s63) -- (s73);
|
||||
|
||||
\draw[activeedge] (s72) -- (s80);
|
||||
\draw[activeedge] (s72) -- (s81);
|
||||
\draw[activeedge] (s73) -- (s82);
|
||||
\draw[activeedge] (s73) -- (s83);
|
||||
|
||||
\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:{$\frac{1}{1}$}] {};
|
||||
\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 (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] {$\times$};
|
||||
|
||||
\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 (6.5,0) [text=red] {$\times$};
|
||||
\node at (6.5,0.5) [text=red] {$\times$};
|
||||
\node at (6.5,1.5) [text=red] {$\times$};
|
||||
\node at (6.5,2) [text=red] {$\times$};
|
||||
\node at (5.5,1) [text=red] {$\times$};
|
||||
\node at (5.5,1.5) [text=red] {$\times$};
|
||||
\node at (4.5,1.5) [text=red] {$\times$};
|
||||
\node at (2.5,2.5) [text=red] {$\times$};
|
||||
|
||||
\node at (8,0) [highlight,label=left:{$\frac{2}{0}$}] {$\frac61$};
|
||||
\node at (8,1) [highlight,label=left:{$\frac{0}{2}$}] {$\frac43$};
|
||||
\node at (8,2) [highlight,label=left:{$\frac{1}{1}$}] {$\frac54$};
|
||||
\node at (8,3) [highlight,label=left:{$\frac{1}{1}$}] {$\frac54$};
|
||||
|
||||
\node at (7.5,0) [text=red] {$\times$};
|
||||
\node at (7.5,0.5) [text=red] {$\times$};
|
||||
\node at (7.5,1.5) [text=red] {$\times$};
|
||||
\node at (7.5,2) [text=red] {$\times$};
|
||||
\node at (6.5,1) [text=red] {$\times$};
|
||||
\node at (3.5,2.5) [text=red] {$\times$};
|
||||
\node at (1.5,2) [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}
|
||||
\trellisIn{6}{01}
|
||||
\trellisIn{7}{11}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=8$.}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\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}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
\draw[activeedge] (s00) -- (s11);
|
||||
\draw[activeedge] (s11) -- (s22);
|
||||
\draw[activeedge] (s22) -- (s31);
|
||||
|
||||
\draw[activeedge] (s31) -- (s43);
|
||||
|
||||
\draw[activeedge] (s43) -- (s53);
|
||||
|
||||
\draw[activeedge] (s53) -- (s63);
|
||||
|
||||
\draw[activeedge] (s63) -- (s72);
|
||||
|
||||
\draw[activeedge] (s72) -- (s80);
|
||||
\draw[activeedge] (s72) -- (s81);
|
||||
|
||||
\draw[activeedge] (s80) -- (s90);
|
||||
\draw[activeedge] (s80) -- (s91);
|
||||
\draw[activeedge] (s81) -- (s93);
|
||||
\draw[activeedge] (s81) -- (s92);
|
||||
|
||||
\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:{$\frac{1}{1}$}] {};
|
||||
\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 (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] {$\times$};
|
||||
|
||||
\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 (6.5,0) [text=red] {$\times$};
|
||||
\node at (6.5,0.5) [text=red] {$\times$};
|
||||
\node at (6.5,1.5) [text=red] {$\times$};
|
||||
\node at (6.5,2) [text=red] {$\times$};
|
||||
\node at (5.5,1) [text=red] {$\times$};
|
||||
\node at (5.5,1.5) [text=red] {$\times$};
|
||||
\node at (4.5,1.5) [text=red] {$\times$};
|
||||
\node at (2.5,2.5) [text=red] {$\times$};
|
||||
|
||||
\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 (7.5,0) [text=red] {$\times$};
|
||||
\node at (7.5,0.5) [text=red] {$\times$};
|
||||
\node at (7.5,1.5) [text=red] {$\times$};
|
||||
\node at (7.5,2) [text=red] {$\times$};
|
||||
\node at (6.5,1) [text=red] {$\times$};
|
||||
\node at (3.5,2.5) [text=red] {$\times$};
|
||||
\node at (1.5,2) [text=red] {$\times$};
|
||||
|
||||
\node at (9,0) [highlight,label=left:{$\frac{2}{0}$}] {$\frac34$};
|
||||
\node at (9,1) [highlight,label=left:{$\frac{0}{2}$}] {$\frac16$};
|
||||
\node at (9,2) [highlight,label=left:{$\frac{1}{1}$}] {$\frac45$};
|
||||
\node at (9,3) [highlight,label=left:{$\frac{1}{1}$}] {$\frac45$};
|
||||
|
||||
\node at (8.5,1) [text=red] {$\times$};
|
||||
\node at (8.5,1.5) [text=red] {$\times$};
|
||||
\node at (8.5,2.5) [text=red] {$\times$};
|
||||
\node at (8.5,3) [text=red] {$\times$};
|
||||
\node at (7.5,2.5) [text=red] {$\times$};
|
||||
\node at (7.5,3) [text=red] {$\times$};
|
||||
\node at (6.5,3) [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}
|
||||
\trellisIn{6}{01}
|
||||
\trellisIn{7}{11}
|
||||
\trellisIn{8}{11}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Сегмент решетки декодера от $t=0$, до $t=9$.}
|
||||
\end{figure}
|
||||
|
||||
\begin{landscape}
|
||||
\begin{figure}
|
||||
\begin{tikzpicture}[x=1.4cm, 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,...,12} {
|
||||
\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,...,11} {
|
||||
\foreach \y in {0,...,3} {
|
||||
\trellisEdges{\x}{\y}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
\draw[activeedge] (s00) -- (s11);
|
||||
\draw[activeedge] (s11) -- (s22);
|
||||
\draw[activeedge] (s22) -- (s31);
|
||||
|
||||
\draw[activeedge] (s31) -- (s43);
|
||||
|
||||
\draw[activeedge] (s43) -- (s53);
|
||||
|
||||
\draw[activeedge] (s53) -- (s63);
|
||||
|
||||
\draw[activeedge] (s63) -- (s72);
|
||||
|
||||
\draw[activeedge] (s72) -- (s80);
|
||||
|
||||
\draw[activeedge] (s80) -- (s91);
|
||||
|
||||
\draw[activeedge] (s91) -- (10,2);
|
||||
\draw[activeedge] (s91) -- (10,3);
|
||||
|
||||
\draw[activeedge] (10,2) -- (11,0);
|
||||
\draw[activeedge] (10,3) -- (11,2);
|
||||
\draw[activeedge] (10,3) -- (11,3);
|
||||
|
||||
\draw[activeedge] (11,0) -- (12,0);
|
||||
\draw[activeedge] (11,2) -- (12,1);
|
||||
\draw[activeedge] (11,3) -- (12,2);
|
||||
\draw[activeedge] (11,3) -- (12,3);
|
||||
|
||||
\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:{$\frac{1}{1}$}] {};
|
||||
\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 (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] {$\times$};
|
||||
|
||||
\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 (6.5,0) [text=red] {$\times$};
|
||||
\node at (6.5,0.5) [text=red] {$\times$};
|
||||
\node at (6.5,1.5) [text=red] {$\times$};
|
||||
\node at (6.5,2) [text=red] {$\times$};
|
||||
\node at (5.5,1) [text=red] {$\times$};
|
||||
\node at (5.5,1.5) [text=red] {$\times$};
|
||||
\node at (4.5,1.5) [text=red] {$\times$};
|
||||
\node at (2.5,2.5) [text=red] {$\times$};
|
||||
|
||||
\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 (7.5,0) [text=red] {$\times$};
|
||||
\node at (7.5,0.5) [text=red] {$\times$};
|
||||
\node at (7.5,1.5) [text=red] {$\times$};
|
||||
\node at (7.5,2) [text=red] {$\times$};
|
||||
\node at (6.5,1) [text=red] {$\times$};
|
||||
\node at (3.5,2.5) [text=red] {$\times$};
|
||||
\node at (1.5,2) [text=red] {$\times$};
|
||||
|
||||
\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:{$\frac{1}{1}$}] {};
|
||||
|
||||
\node at (8.5,1) [text=red] {$\times$};
|
||||
\node at (8.5,1.5) [text=red] {$\times$};
|
||||
\node at (8.5,2.5) [text=red] {$\times$};
|
||||
\node at (8.5,3) [text=red] {$\times$};
|
||||
\node at (7.5,2.5) [text=red] {$\times$};
|
||||
\node at (7.5,3) [text=red] {$\times$};
|
||||
\node at (6.5,3) [text=red] {$\times$};
|
||||
|
||||
\node at (10, 0) [highlight,label=left:{$\frac{1}{1}$}] {$\frac45$};
|
||||
\node at (10, 1) [highlight,label=left:{$\frac{1}{1}$}] {$\frac45$};
|
||||
\node at (10, 2) [highlight,label=left:{$\frac{2}{0}$}] {$\frac34$};
|
||||
\node at (10, 3) [highlight,label=left:{$\frac{0}{2}$}] {$\frac16$};
|
||||
|
||||
\node at (9.5,1) [text=red] {$\times$};
|
||||
\node at (9.5,1.5) [text=red] {$\times$};
|
||||
\node at (9.5,2.5) [text=red] {$\times$};
|
||||
\node at (9.5,3) [text=red] {$\times$};
|
||||
|
||||
\node at (11, 0) [highlight,label=left:{$\frac{2}{0}$}] {$\frac63$};
|
||||
\node at (11, 1) [highlight,label=left:{$\frac{0}{2}$}] {$\frac45$};
|
||||
\node at (11, 2) [highlight,label=left:{$\frac{1}{1}$}] {$\frac52$};
|
||||
\node at (11, 3) [highlight,label=left:{$\frac{1}{1}$}] {$\frac52$};
|
||||
|
||||
\node at (10.5,0) [text=red] {$\times$};
|
||||
\node at (10.5,1.5) [text=red] {$\times$};
|
||||
\node at (10.5,2) [text=red] {$\times$};
|
||||
|
||||
\node at (12, 0) [highlight,label=left:{$\frac{0}{2}$}] {$\frac34$};
|
||||
\node at (12, 1) [highlight,label=left:{$\frac{2}{0}$}] {$\frac52$};
|
||||
\node at (12, 2) [highlight,label=left:{$\frac{1}{1}$}] {$\frac53$};
|
||||
\node at (12, 3) [highlight,label=left:{$\frac{1}{1}$}] {$\frac53$};
|
||||
|
||||
\node at (11.5,1) [text=red] {$\times$};
|
||||
\node at (11.5,0.5) [text=red] {$\times$};
|
||||
\node at (11.5,1.5) [text=red] {$\times$};
|
||||
\node at (11.5,2) [text=red] {$\times$};
|
||||
\node at (10.5,0.5) [text=red] {$\times$};
|
||||
\node at (9.5,0) [text=red] {$\times$};
|
||||
\node at (9.5,0.5) [text=red] {$\times$};
|
||||
\node at (8.5,0) [text=red] {$\times$};
|
||||
\node at (8.5,2) [text=red] {$\times$};
|
||||
\node at (2.5,3) [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}
|
||||
\trellisIn{6}{01}
|
||||
\trellisIn{7}{11}
|
||||
\trellisIn{8}{11}
|
||||
\trellisIn{9}{10}
|
||||
\trellisIn{10}{11}
|
||||
\trellisIn{11}{00}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Полная решетка декодера.}
|
||||
\end{figure}
|
||||
\end{landscape}
|
||||
|
||||
BIN
term_paper.pdf
BIN
term_paper.pdf
Binary file not shown.
311
term_paper.tex
311
term_paper.tex
@@ -13,9 +13,11 @@
|
||||
\usetikzlibrary{shapes.misc}
|
||||
\usepackage{pdflscape}
|
||||
\usepackage{float}
|
||||
\usepackage{pgfplots}
|
||||
|
||||
\DeclareSymbolFont{T2Aletters}{T2A}{cmr}{m}{it}
|
||||
\graphicspath{ {./images/} }
|
||||
\pgfplotsset{width=10cm,compat=1.9}
|
||||
|
||||
% Установки для отрисовки решеток кодера
|
||||
\tikzstyle{lightedge}=[dashed]
|
||||
@@ -56,16 +58,115 @@
|
||||
|
||||
|
||||
\author{Анатолий Копыл}
|
||||
\title{Курсовая работа}
|
||||
\title{Расчёт основных характеристик цифровой системы связи с использованием квадратурной модуляции}
|
||||
|
||||
\begin{document}
|
||||
|
||||
% НАЧАЛО ТИТУЛЬНОГО ЛИСТА
|
||||
\makeatletter
|
||||
\begin{titlepage}
|
||||
\begin{center}
|
||||
\hfill \break
|
||||
\footnotesize{ФЕДЕРАЛЬНОЕ ГОСУДАРСТВЕННОЕ БЮДЖЕТНОЕ ОБРАЗОВАТЕЛЬНОЕ УЧРЕЖДЕНИЕ}\\
|
||||
\footnotesize{ВЫСШЕГО ПРОФЕССИОНАЛЬНОГО ОБРАЗОВАНИЯ}\\
|
||||
\small{\textbf{«Санкт-Петербургский государственный университет телекоммуникаций им. проф. М. А. Бонч-Бруевича»}}\\
|
||||
\hfill \break
|
||||
\normalsize{Факультет инфокоммуникационных сетей и систем}\\
|
||||
\hfill \break
|
||||
\normalsize{Кафедра теоретических основ связи и радиотехники}\\
|
||||
\hfill\break
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\large{ \@title }\\
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\normalsize{Учебная дисциплина <<Теория электрической связи>>}\\
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\normalsize{Курсовая работа}\\
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
\end{center}
|
||||
|
||||
\hfill \break
|
||||
\hfill \break
|
||||
|
||||
\normalsize{
|
||||
\hfill\begin{minipage}{\dimexpr\textwidth-6cm}
|
||||
Студент группы ИКТО-91 Копыл А. В.\\
|
||||
зачетная книжка № 1905141\\\\
|
||||
Руководитель \underline{\hspace{4cm}}
|
||||
\end{minipage}
|
||||
}\\
|
||||
\vfill
|
||||
\begin{center} Санкт-Петербург 2021 \end{center}
|
||||
\thispagestyle{empty} % выключаем отображение номера для этой страницы
|
||||
\end{titlepage}
|
||||
\makeatother
|
||||
% КОНЕЦ ТИТУЛЬНОГО ЛИСТА
|
||||
|
||||
\newpage
|
||||
|
||||
Цель курсовой работы -- изучить и разработать систему цифровой связи,
|
||||
оптимальную в отношении флуктуационной помехи и исключающую появления
|
||||
межсимвольной помехи.
|
||||
|
||||
\section{Структурная схема системы\\цифровой связи}
|
||||
|
||||
Система связи предназначена для передачи аналоговых сообщений
|
||||
по цифровому каналу связи.
|
||||
\begin{figure}[H]
|
||||
\includegraphics[scale=0.5]{struct_scheme}
|
||||
\caption{Структурная схема цифровой системы связи}
|
||||
\label{fig:struct_scheme}
|
||||
\end{figure}
|
||||
|
||||
В систему входят следующие функциональные узлы с последующими назначениями:
|
||||
\begin{enumerate}
|
||||
\item Источник сообщений -- создает реализации $a(t)$ случайного
|
||||
процесса $A(t)$.
|
||||
\item Аналого-цифровой преобразователь -- преобразует аналоговый
|
||||
сигнал от источника сообщения в последовательность
|
||||
двоичных отсчетов $b(t)$.
|
||||
\item Кодер -- включает в цифровой поток от АЦП дополнительные
|
||||
символы, предназначенные для повышения помехоустойчивости системы
|
||||
связи;
|
||||
\item Формирователь модулирующих символов -- служит для получения
|
||||
модулирующих сигналов $I(t)$ и $Q(t)$, соответствующих заданному
|
||||
виду модуляции;
|
||||
\item Сглаживающие формирующие фильтры (СФФ1, СФФ2);
|
||||
\item Перемножители -- для получения БМ сигналов: синфазного
|
||||
$I(t)\cos{\omega_Ct}$ и квадратурного $Q(t)\sin{\omega_Ct}$.
|
||||
\item Фазовращатель -- для получения второго несущего колебания,
|
||||
ортогонального по отношению к первому;
|
||||
\item Генератор гармонических колебаний -- для получения несущего
|
||||
колебания;
|
||||
\item Инвертор;
|
||||
\item Сумматор -- для объединения синфазного и квадратурного
|
||||
сигналов в единый сигнал с квадратурной модуляцией
|
||||
$S_{КАМ}(t) = I(t)\cos{\omega_Ct} + Q(t)\sin{\omega_Ct}$;
|
||||
\item Непрерывный канал -- среда распространения сигнала
|
||||
$S_{КАМ}(t)$;
|
||||
\item Демодулятор -- для анализа приходящего сигнала,
|
||||
искаженного помехами, и принятии решения о переданном сообщении;
|
||||
\item Преобразователь параллельного кода в последовательный код --
|
||||
для преобразования сигнала с выхода демодулятора в
|
||||
последовательный формат кодовых комбинаций;
|
||||
\item Декодер -- для исправления части ошибок, возникших при приёме
|
||||
сообщения $\hat{b}(t)$ вследствие влияния помех;
|
||||
\item Цифро-аналоговый преобразователь -- для восстановления
|
||||
аналоговой формы сигнала $\hat{a}(t)$ из его цифрового представления;
|
||||
\item Получатель сообщений.
|
||||
\end{enumerate}
|
||||
|
||||
\section{Исходные данные}
|
||||
\[ m=41 \]
|
||||
$m=41$
|
||||
\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 \\
|
||||
Предельные уровни аналогового сигнала \(a_{мин}\), \(a_{макс}\) (В) & \(a_{макс}=25,6\) В;\newline\(a_{мин}=-25,6\) 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
|
||||
@@ -73,20 +174,207 @@
|
||||
\hline
|
||||
Спектральная плотность мощности флуктуационной помехи & 41 & \(N_0=2,3\cdot 10^{-7}\, В^2/Гц\)\\
|
||||
\hline
|
||||
q - номер тактового интервала ошибки & \(q=m\mod{3}+1\) & \(q=3\)\\
|
||||
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}
|
||||
\section{Расчет составляющих системы цифровой связи}
|
||||
|
||||
\subsection{Источник сообщений}
|
||||
Источник сообщения (ИС) вырабатывает реализации $a(t)$ стационарного
|
||||
случайного процесса $A(t)$, типа квазибелого шума с параметрами
|
||||
$a_{мин}$, $a_{макс}$ и $f_В$. Мгновенные значения сообщения
|
||||
равновероятны в интервале от значения $a_{мин}$ и до значения
|
||||
$a_{макс}$.
|
||||
|
||||
Требуется:
|
||||
\begin{enumerate}
|
||||
\item Написать аналитические выражения для плотности вероятности
|
||||
$w(а)$ мгновенных значений сообщения, функции распределения $F(a)$ и
|
||||
построить их графики (рис. \ref{fig:prob_plots}).
|
||||
|
||||
\[ w(a)=\frac{1}{a_{макс}-a_{мин}}=\frac1\Delta=\frac{1}{25,6+25,6}=0,02 \]
|
||||
\[ F(a)=\int^a_{-\infty}w(a)da=
|
||||
\int^a_{a_{мин}}\frac{1}{\Delta}da=
|
||||
\begin{cases}
|
||||
1, & a > a_{макс}\\
|
||||
\frac{a-a_{мин}}{\Delta}, & a_{мин} \leq a \leq a_{макс}\\
|
||||
0, & a < a_{мин}
|
||||
\end{cases}\]
|
||||
где $\Delta = a_{макс}-a_{мин}=51,2\, В$.
|
||||
|
||||
% Графики
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\pgfmathsetmacro{\amin}{-25.6}
|
||||
\pgfmathsetmacro{\amax}{25.6}
|
||||
\begin{axis}[
|
||||
width=6cm,height=4cm,
|
||||
axis lines = left,
|
||||
xlabel = $a$,
|
||||
ylabel = {$F(a)$},
|
||||
xmin=-40, xmax=40,
|
||||
ymin=0, ymax=1.25,
|
||||
]
|
||||
\addplot [
|
||||
domain=-40:\amin,
|
||||
color=red,
|
||||
]
|
||||
{0};
|
||||
\addplot [
|
||||
domain=\amin:\amax,
|
||||
samples=2,
|
||||
color=red,
|
||||
]
|
||||
{(x-\amin) / 51.2};
|
||||
\addplot [
|
||||
domain=\amax:40,
|
||||
color=red,
|
||||
]
|
||||
{1};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
\begin{tikzpicture}
|
||||
\pgfmathsetmacro{\amin}{-25.6}
|
||||
\pgfmathsetmacro{\amax}{25.6}
|
||||
\begin{axis}[
|
||||
width=6cm,height=4cm,
|
||||
axis lines = left,
|
||||
xlabel = $a$,
|
||||
ylabel = {$w(a)$},
|
||||
xmin=-40, xmax=40,
|
||||
ymin=0, ymax=0.03,
|
||||
]
|
||||
\addplot [
|
||||
domain=-40:\amin,
|
||||
color=blue,
|
||||
]
|
||||
{0};
|
||||
\addplot [
|
||||
domain=\amin:\amax,
|
||||
samples=2,
|
||||
color=blue,
|
||||
]
|
||||
{0.02};
|
||||
\addplot [
|
||||
domain=\amax:40,
|
||||
color=blue,
|
||||
]
|
||||
{0};
|
||||
\draw [dashed] (axis cs:\amin,0) -- (axis cs:\amin,0.02);
|
||||
\draw [dashed] (axis cs:\amax,0) -- (axis cs:\amax,0.02);
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\caption{Графики функции распределения и плотности вероятности}
|
||||
\label{fig:prob_plots}
|
||||
\end{figure}
|
||||
\item Рассчитать математическое ожидание $\overline{A(t)}$ и
|
||||
дисперсию $D\{A(t)\}$ сообщения $A(t)$.
|
||||
\[ \overline{A(t)}=\int^\infty_{-\infty}a\cdot w(a)da=
|
||||
\int^{a_{макс}}_{a_{мин}}a \frac{1}{a_{макс}-a_{мин}} da=
|
||||
\frac{a^2}{2\Delta} \Biggr|^{a_{макс}}_{a_{мин}}\! =
|
||||
\frac{a_{макс}^2-a_{мин}^2}{2\Delta}=0 \]
|
||||
|
||||
\begin{align*}\begin{split}
|
||||
D\{A(t)\}&=\int^\infty_{-\infty}(a-\overline{A(t)})^2 w(a)da=
|
||||
\int^{a_{макс}}_{a_{мин}}a^2w(a)da\\
|
||||
&=\frac{a^3}{3\Delta}\Biggr|^{a_{макс}}_{a_{мин}}\!
|
||||
=\frac{a_\text{min}^2+a_\text{max}a_\text{min}+a_\text{max}^2}{3}
|
||||
=218,5
|
||||
\end{split}\end{align*}
|
||||
\item Написать аналитическое выражение для спектральной плотности
|
||||
мощности $G_A(f)$ сообщения $A(t)$ и построить график
|
||||
(рис. \ref{fig:spectr_plot}).
|
||||
\[ G_A(f)=\frac{D\{A(t)\}}{2f_В}=\frac{218,5}{2\cdot1,41\cdot 10^4}
|
||||
=7,7 \,мВ^2/Гц \]
|
||||
\[ G_A(f)=\begin{cases}
|
||||
7,7 \,мВ^2/Гц, & |f| \leq f_B\\
|
||||
0, & |f| > f_B
|
||||
\end{cases} \]
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\pgfmathsetmacro{\fv}{14100}
|
||||
\pgfmathsetmacro{\Gaf}{0.0077}
|
||||
\begin{axis}[
|
||||
width=6cm,height=4cm,
|
||||
axis lines = left,
|
||||
ylabel = {$G_A(f)$},
|
||||
xmin=-\fv*1.5, xmax=\fv*1.5,
|
||||
ymin=0, ymax=\Gaf*1.5,
|
||||
]
|
||||
\addplot [
|
||||
domain=-\fv*1.5:-\fv,
|
||||
color=blue,
|
||||
]
|
||||
{0};
|
||||
\addplot [
|
||||
domain=-\fv:\fv,
|
||||
samples=2,
|
||||
color=blue,
|
||||
]
|
||||
{\Gaf};
|
||||
\addplot [
|
||||
domain=\fv:\fv*1.5,
|
||||
color=blue,
|
||||
]
|
||||
{0};
|
||||
\draw [dashed] (axis cs:-\fv,0) -- (axis cs:-\fv,\Gaf);
|
||||
\draw [dashed] (axis cs:\fv,0) -- (axis cs:\fv,\Gaf);
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\caption{График спектральной плотности мощности.}
|
||||
\label{fig:spectr_plot}
|
||||
\end{figure}
|
||||
\item Найти аналитическое выражение для корреляционной функции
|
||||
$B_A(\tau)$ сообщения $A(t)$ и построить график
|
||||
(рис. \ref{fig:coorel_plot}).
|
||||
По форме графика $B_A(\tau)$ определить,
|
||||
является ли сообщение $A(t)$ эргодическим случайным процессом
|
||||
или не является таковым.
|
||||
|
||||
\begin{align*}\begin{split}
|
||||
B_A(\tau)&=\int^\infty_{-\infty}\frac{G_A(f)}{2}e^{j2\pi f\tau}df
|
||||
=\int^{f_B}_{-f_B}\frac{G_A}{2}\cos{2\pi f\tau}df\\
|
||||
&=\frac{G_A}2 \frac{\sin{2\pi f \tau}}{2\pi \tau}\Biggr|^{f_B}_{-f_B}
|
||||
=G_A\frac{\sin{2\pi f_B \tau}}{2\pi\tau}
|
||||
\end{split}\end{align*}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\pgfmathsetmacro{\PI}{3.14159}
|
||||
\pgfmathsetmacro{\fv}{14100}
|
||||
\pgfmathsetmacro{\Ga}{0.0077}
|
||||
\begin{axis}[
|
||||
width=10cm,height=6cm,
|
||||
axis lines = left,
|
||||
ylabel = {$B_A(\tau)$},
|
||||
xlabel = {$\tau$},
|
||||
]
|
||||
\addplot [
|
||||
color=blue,
|
||||
samples=100,
|
||||
domain=-0.01:0.01,
|
||||
]
|
||||
{\Ga*(sin(2*\PI*\fv*x))/(2*\PI*x)};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\caption{График корреляционной функции $B_A(\tau)$.}
|
||||
\label{fig:coorel_plot}
|
||||
\end{figure}
|
||||
\end{enumerate}
|
||||
|
||||
\subsection{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}
|
||||
\subsection{Кодер}
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.8]{coder}
|
||||
|
||||
@@ -99,7 +387,7 @@
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\subsection{Решетка кодера}
|
||||
\subsubsection{Решетка кодера}
|
||||
|
||||
\input{coder}
|
||||
|
||||
@@ -107,13 +395,16 @@
|
||||
\[T_В=\frac{\Delta t}{2k}=\frac{3,546\cdot 10^{-5}}{2\cdot 9}=
|
||||
1,97\cdot 10^{-6}\,с\]
|
||||
|
||||
\section{Декодер}
|
||||
\subsection{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.
|
||||
\(\overline{Z}=11 \overset{\times}{0} 0 00 01 10 10 01 11 11\). Крестиком обозначен ошибочно принятый символ.
|
||||
|
||||
\subsection{Диаграмма декодера}
|
||||
\subsubsection{Диаграмма декодера}
|
||||
\input{decoder}
|
||||
|
||||
Наложив полученный путь на решетку кодера, узнаем декодированное слово.
|
||||
$\overline{m}_{получ}=101111001$
|
||||
|
||||
\end{document}
|
||||
|
||||
Reference in New Issue
Block a user