mirror of
https://github.com/eddyem/lectures.git
synced 2025-12-06 02:35:18 +03:00
254 lines
9.5 KiB
TeX
254 lines
9.5 KiB
TeX
\documentclass[a4paper,12pt]{extarticle}
|
||
\usepackage{/home/eddy/ed}
|
||
\title{ðÒÁËÔÉËÕÍ \No2: ÓÔÁÔÉÓÔÉËÁ É ×ÅÒÏÑÔÎÏÓÔØ}
|
||
\author{}\date{}\nocolon
|
||
|
||
\long\def\task#1{\noindent\leavevmode\refstepcounter{sect}\llap{\textbf{\thesect}\;}\indent\textit{#1}}
|
||
\def\t#1{{\upshape\ttfamily #1}}
|
||
|
||
\begin{document}
|
||
\maketitle
|
||
\section{÷×ÅÄÅÎÉÅ × Octave}
|
||
óÐÒÁ×ËÁ: \verb'help ËÏÍÁÎÄÁ'.
|
||
|
||
óÌÕÞÁÊÎÙÅ ÞÉÓÌÁ: \verb'rand(rows, cols)'~--- ÒÁ×ÎÏÍÅÒÎÏÅ ÒÁÓÐÒÅÄÅÌÅÎÉÅ,
|
||
\verb'randn(rows, cols)'~--- ÎÏÒÍÁÌØÎÏÅ, \verb'rande'~--- ÜËÓÐÏÎÅÎÃÉÁÌØÎÏÅ, \verb'randg'~---
|
||
ÇÁÍÍÁ-ÒÁÓÐÒÅÄÅÌÅÎÉÅ, \verb'randp'~--- ðÕÁÓÓÏÎ.
|
||
|
||
\subsection{íÁÔÒÉÃÙ É ×ÅËÔÏÒÙ}
|
||
óÏÚÄÁÎÉÅ ×ÅËÔÏÒÏ×: \verb'A=[1 2 3]' ÉÌÉ ÖÅ \verb'A=[1,2,3]'. ÷ÅËÔÏÒ-ÓÔÏÌÂÅÃ: \verb|A=[1 2 3]'| ÉÌÉ
|
||
ÖÅ \verb'A=[1;2;3]'. \verb'A=[ÎÁÞÚÎ.:<ÛÁÇ:>ËÏÎÚÎ.]'.
|
||
|
||
óÏÚÄÁÎÉÅ ÍÁÔÒÉÃ: \verb'A=[1 5 2; 4 1 0]'. ëÏÎËÁÔÅÎÁÃÉÑ: \verb'A=[1:3]', \verb'B=[6:8]',
|
||
\verb'C=[12:14]'; \verb'D=[A;B;C]'. éÌÉ: \verb|A=[1:3]'|, \verb|B=[6:8]'|,
|
||
\verb|C=[12:14]'|; \verb'D=[A B C]'. ëÏÎËÁÔÅÎÁÃÉÑ ×ÏÚÍÏÖÎÁ É ÄÌÑ ×ÅËÔÏÒÏ× É ÍÁÔÒÉÃ:
|
||
\verb|E=[(20:22)' (11:13)']|, \verb'[D E]'. \verb'X=[4 3 2]', \verb'Y=[9 8 7]', \verb'Z=[X Y]'.
|
||
|
||
òÁÚÍÅÒ × ÜÌÅÍÅÎÔÁÈ: \verb'numel(A)'. òÁÚÍÅÒ × ÂÁÊÔÁÈ: \verb'sizeof(A)'. òÁÚÍÅÒÎÏÓÔØ: \verb'size(A)'.
|
||
|
||
ðÏÓÍÏÔÒÅÔØ ÚÎÁÞÅÎÉÅ ÐÅÒÅÍÅÎÎÏÊ ÍÏÖÎÏ, ÕËÁÚÁ× ÅÅ ÉÍÑ ÉÌÉ ÖÅ ËÏÍÁÎÄÕ \verb'disp(X)'.
|
||
|
||
óÐÅÃÉÁÌØÎÙÅ ÍÁÔÒÉÃÙ: \verb'eye(x)', \verb'ones(x)', \verb'zeros(x)',
|
||
\verb'repmat(matrix, [ycount xcount])', \verb'magic(x)'.
|
||
\textbf{ðÅÒ×ÁÑ ËÏÏÒÄÉÎÁÔÁ~--- Y!}
|
||
|
||
óÐÉÓÏË ÐÅÒÅÍÅÎÎÙÈ: \verb'whos'. õÄÁÌÉÔØ ÐÅÒÅÍÅÎÎÙÅ: \verb'clear'.
|
||
|
||
\textbf{éÎÄÅËÓÙ~--- Ó ÅÄÉÎÉÃÙ!} éÎÄÅËÓÁÃÉÑ: \verb'X=magic(5)', \verb'X(1:2,3:5)',
|
||
\verb'X(2:end,3:end)', \verb'X(:,3)', \verb'X(3,:)', \verb'magic(4)(:,1)'.
|
||
|
||
íÁÔÒÉÃÕ~--- × ÓÔÏÌÂÅÃ: \verb'magic(4)(:)'.
|
||
|
||
õÄÁÌÅÎÉÅ ÜÌÅÍÅÎÔÏ× ÍÁÔÒÉÃ É ×ÅËÔÏÒÏ×: \verb'vec=[1:10]', \verb'idx=[3,7,5]', \verb'vec[idx]=[]';
|
||
\verb'X(:,[1,3])=[]'.
|
||
|
||
\subsection{íÁÔÒÉÞÎÙÅ É ×ÅËÔÏÒÎÙÅ ÏÐÅÒÁÃÉÉ}
|
||
óÌÏÖÅÎÉÅ, ×ÙÞÉÔÁÎÉÅ: \verb'A+B', \verb'A-B'.
|
||
|
||
ôÒÁÎÓÐÏÎÉÒÏ×ÁÎÉÅ, ÓÏÐÒÑÖÅÎÉÅ: \verb|A'|. óÔÅÐÅÎØ (ÄÌÑ Ë×ÁÄÒÁÔÎÙÈ ÍÁÔÒÉÃ): \verb'X^n'.
|
||
\textbf{ïÔÒÉÃÁÔÅÌØÎÁÑ ÓÔÅÐÅÎØ}: \verb'A^(-1)==inv(A)', ÎÏ \verb'A^(-2)==inv(A)^2'!
|
||
\textbf{ðÏÜÌÅÍÅÎÔÎÙÅ ÏÐÅÒÁÃÉÉ}: \verb'A.(op)'. õÍÎÏÖÅÎÉÅ ÍÁÔÒÉÃ: \verb'A*B', ÎÁÐÒÉÍÅÒ,
|
||
\begin{verbatim}
|
||
A=[1 4 7; 8 5 2];
|
||
B=[4 5; 9 6; 3 1];
|
||
X=A*B
|
||
ans =
|
||
61 36
|
||
83 72
|
||
\end{verbatim}
|
||
|
||
\verb'A=[1 2; 3 4]', \verb'B=[50 60; 70 80]'.
|
||
íÁÔÒÉÞÎÏÅ ÄÅÌÅÎÉÅ: \verb'A/B' (\verb'(A/B)*B==A'), ÜË×É×ÁÌÅÎÔÎÏ $AB^{-1}$. <<ìÅ×ÏÅ>> ÄÅÌÅÎÉÅ:
|
||
\verb'A\B' (\verb'A*(A\B)==B'), ÜË×É×ÁÌÅÎÔÎÏ $A^{-1}B$.
|
||
|
||
\subsection{çÒÁÆÉËÉ}
|
||
\verb'x=[0:0.1:2*pi]', \verb'plot(sin(x))'.
|
||
|
||
óÏÈÒÁÎÉÔØ ÇÒÁÆÉË: \verb'print -dpdf plot.pdf'.
|
||
|
||
çÉÓÔÏÇÒÁÍÍÁ: \verb'hist(x,N)'. îÁÐÒÉÍÅÒ,
|
||
\begin{verbatim}
|
||
x=rand(1,10000);
|
||
hist(x);
|
||
hist(x, 5);
|
||
x=randn(1,10000);
|
||
hist(x,20);
|
||
\end{verbatim}
|
||
|
||
çÒÁÆÉËÉ Ä×ÕÍÅÒÎÙÈ ÆÕÎËÃÉÊ. \verb'[X,Y]=meshgrid(-5:0.1:5,-6:0.1:6);', \verb'Z=X.^2-4*Y.^2;',
|
||
\verb'surf(X,Y,Z)'. \verb'surfc(X,Y,Z)'~--- Ó ÉÚÏÌÉÎÉÑÍÉ. \verb'mesh(X,Y,Z)'.
|
||
|
||
úÁËÒÙÔØ ÇÒÁÆÉË: \verb'close all' ÉÌÉ ÖÅ \verb'close(fig)'. \verb'P=figure(N);'. ÷ÙÂÏÒ ÍÅÖÄÕ ÔÅËÕÝÉÍ
|
||
ÇÒÁÆÉËÏÍ ÄÌÑ ÏÔÏÂÒÁÖÅÎÉÑ: \verb'figure(N)'. îÁÐÒÉÍÅÒ:
|
||
\begin{verbatim}
|
||
P1=figure(1); P2=figure(2);
|
||
mesh(X,Y,Z);
|
||
figure(1);
|
||
surfc(X,Y,Z);
|
||
close(P2);
|
||
\end{verbatim}
|
||
|
||
\verb'hold on/off'~--- ÄÏÒÉÓÏ×ÁÔØ ÞÔÏ-ÔÏ ÎÁ ÇÒÁÆÉËÅ.
|
||
|
||
îÏ ÉÎÔÅÒÆÅÊÓ Octave Ë gnuplot ÎÅ ÓÒÁ×ÎÉÔÓÑ Ó ÓÁÍÉÍ gnuplot (ÐÒÉÍÅÒ)!
|
||
|
||
ðÏÓÔÒÏÉÍ ÇÒÁÆÉË ÐÌÏÔÎÏÓÔÉ ×ÅÒÏÑÔÎÏÓÔÉ ÎÏÒÍÁÌØÎÏÇÏ ÒÁÓÐÒÅÄÅÌÅÎÉÑ ×ÅÌÉÞÉÎÙ Ó $\mean{X}=-20$ É
|
||
$\sigma_X=20$: \verb'x=[-70:30]; y=normpdf(x,-20,20);'.
|
||
|
||
\subsection{ãÉËÌÙ, ÕÓÌÏ×ÉÑ}
|
||
ãÉËÌ \verb'for'. \verb'for x=1:10; printf("x=%d\n", x); endfor'.
|
||
|
||
\begin{verbatim}
|
||
X=[]; Y=[]; for x=1:3; A=dlmread(sprintf("for%02d", x));
|
||
> X=[X; A(:,1)]; Y=[Y; A(:,2)]; endfor
|
||
plot(X, Y, 'o')
|
||
\end{verbatim}
|
||
|
||
ãÉËÌ \verb'while':
|
||
\begin{verbatim}
|
||
F=1; x=1; while F < 1e10; x+=1; F*=x; endwhile; printf("!%d=%g\n", x, F);
|
||
!14=8.71783e+10
|
||
\end{verbatim}
|
||
|
||
õÓÌÏ×ÉÑ:
|
||
\begin{verbatim}
|
||
x = input("Enter value: ");
|
||
if(x < -5) printf("Less than -5\n")
|
||
>elseif (x > 5) printf("More than 5\n")
|
||
>else printf("Between -5 and 5\n")
|
||
>endif
|
||
\end{verbatim}
|
||
|
||
\subsection{m-ÆÁÊÌÙ}
|
||
æÕÎËÃÉÉ É ÓËÒÉÐÔÙ. æÕÎËÃÉÉ: \verb'checkX.m'.
|
||
|
||
óËÒÉÐÔÙ: \verb'script.m'. óËÒÉÐÔ ×ÙÐÏÌÎÑÅÔÓÑ × ÇÌÏÂÁÌØÎÏÍ ÐÒÏÓÔÒÁÎÓÔ×Å!
|
||
ðÒÉÍÅÒ (ÚÁËÏÍÍÅÎÔÉÒÏ×ÁÔØ \verb'x=' × \verb'script.m'):
|
||
\begin{verbatim}
|
||
clear
|
||
x = [-2*pi:0.1:2*pi];
|
||
script
|
||
\end{verbatim}
|
||
|
||
ðÒÏ×ÅÒËÁ ÐÅÒÅÍÅÎÎÏÊ (É ÎÅ ÔÏÌØËÏ): \verb'exist(name, type)', ÓËÒÉÐÔ \verb'script_chk' (ÚÁÐÕÓÔÉÔØ Ó
|
||
ÏÐÒÅÄÅÌÅÎÎÏÊ \verb'x' É ÐÏÓÌÅ \verb'clear').
|
||
|
||
\subsection{óÔÁÔÉÓÔÉËÁ}
|
||
óÒÅÄÎÅÅ: \verb'mean(x)'. RMS: \verb'std(x)'. íÅÄÉÁÎÁ: \verb'median(x)'. óÕÍÍÁ: \verb'sum(x)'.
|
||
ëÕÍÕÌÑÔÉ×ÎÁÑ ÓÕÍÍÁ: \verb'cumsum(x)'. óÏÒÔÉÒÏ×ËÁ: \verb'sort(x)'.
|
||
|
||
íÉÎÉÍÕÍ, ÍÁËÓÉÍÕÍ: \verb'min(x)', \verb'max(x)'.
|
||
|
||
|
||
\section{ðÒÉÍÅÒÙ ×ÙÐÏÌÎÅÎÉÑ ÚÁÄÁÎÉÊ}
|
||
\task{óÇÅÎÅÒÉÒÏ×ÁÔØ ÓÉÎÕÓÏÉÄÕ ÎÁ ÕÞÁÓÔËÅ~$[0,2\pi]$, ÄÏÂÁ×ÉÔØ Ë ÎÅÊ ÇÁÕÓÓÏ× ÂÅÌÙÊ ÛÕÍ Ó
|
||
ÁÍÐÌÉÔÕÄÏÊ~10\,Äâ. ðÏÓÔÒÏÉÔØ ÇÒÁÆÉË.}
|
||
|
||
óÇÅÎÅÒÉÒÕÅÍ ÓÉÎÕÓÏÉÄÁÌØÎÙÊ ÓÉÇÎÁÌ ÎÁ ÕÞÁÓÔËÅ~$[0,2\pi]$
|
||
ËÏÍÁÎÄÁÍÉ
|
||
$$\verb'x=[0:pi/50:2*pi]; y=sin(x);'$$
|
||
ôÅÐÅÒØ ÄÏÂÁ×ÉÍ Ë ÓÉÇÎÁÌÕ
|
||
ÇÁÕÓÓÏ× ÂÅÌÙÊ ÛÕÍ Ó ÁÍÐÌÉÔÕÄÏÊ 10~Äâ ÏÔÎÏÓÉÔÅÌØÎÏ ÁÍÐÌÉÔÕÄÙ ÓÉÇÎÁÌÁ:
|
||
$$\verb"y1=awgn(y,10,'measured'); plot(x, [y; y1])"$$
|
||
ôÒÅÔÉÊ ÐÁÒÁÍÅÔÒ (measured) ÏÂÑÚÁÔÅÌÅÎ, Ô.Ë. ÂÅÚ ÎÅÇÏ ÐÒÏÃÅÓÓ ÄÏÂÁ×ÌÅÎÉÑ
|
||
ÛÕÍÁ ÂÕÄÅÔ ÎÅÓËÏÌØËÏ ÉÎÙÍ (ÍÏÝÎÏÓÔØ ÓÉÇÎÁÌÁ ÂÕÄÅÔ ÓÞÉÔÁÔØÓÑ ÒÁ×ÎÏÊ 0~Äâ), ÍÏÖÅÔÅ
|
||
ÐÒÏ×ÅÒÉÔØ ÎÁ ÓÉÎÕÓÏÉÄÅ Ó ÁÍÐÌÉÔÕÄÏÊ~10.
|
||
|
||
\task{óÇÅÎÅÒÉÒÏ×ÁÔØ ÓÉÎÕÓÏÉÄÕ Ó ÐÅÒÉÏÄÏÍ $\pi/5$ ÎÁ ÉÎÔÅÒ×ÁÌÅ $[0,20]$ Ó ÁÍÐÌÉÔÕÄÎÏÊ ÍÏÄÕÌÑÃÉÅÊ
|
||
ÐÉÌÏÏÂÒÁÚÎÏÊ ÆÕÎËÃÉÅÊ Ó ÐÅÒÉÏÄÏÍ~10.}
|
||
|
||
äÌÑ ÇÅÎÅÒÁÃÉÉ ÓÉÎÕÓÏÉÄÁÌØÎÏÇÏ ÓÉÇÎÁÌÁ $y_0=A\sin(2\pi t/T)$ Ó ÁÍÐÌÉÔÕÄÎÏÊ ÍÏÄÕÌÑÃÉÅÊ
|
||
ÐÏ ÚÁËÏÎÕ $y_1=f(t)$ ÎÅÏÂÈÏÄÉÍÏ ÐÅÒÅÍÎÏÖÉÔØ ÜÔÉ Ä×Å ÆÕÎËÃÉÉ: $y=y_0\cdot y_1$.
|
||
ðÒÏÍÏÄÕÌÉÒÕÅÍ ÓÉÎÕÓÏÉÄÕ Ó ÐÅÒÉÏÄÏÍ $\pi/5$ ÐÉÌÏÏÂÒÁÚÎÙÍ ÓÉÇÎÁÌÏÍ Ó ÐÅÒÉÏÄÏÍ~10
|
||
ÎÁ ÉÎÔÅÒ×ÁÌÅ $x\in[0,20]$.
|
||
äÌÑ ÇÅÎÅÒÉÒÏ×ÁÎÉÑ <<ÐÉÌÙ>> ÉÓÐÏÌØÚÕÅÔÓÑ ÆÕÎËÃÉÑ \verb'sawtooth'. åÓÌÉ ÚÁÄÁÔØ
|
||
ÅÊ ÏÄÉÎ ÁÒÇÕÍÅÎÔ (×ÅËÔÏÒ $x$), ÐÅÒÉÏÄ ÂÕÄÅÔ ÒÁ×ÅÎ~$2\pi$, Á ÓÉÇÎÁÌ ÂÕÄÅÔ
|
||
ÉÚÍÅÎÑÔØÓÑ × ÉÎÔÅÒ×ÁÌÅ $[-1,1]$. þÔÏÂÙ ÚÁÄÁÔØ ÓÍÅÝÅÎÉÅ ÍÁËÓÉÍÕÍÁ, ÒÁ×ÎÏÅ $a\cdot2\pi$,
|
||
ÎÅÏÂÈÏÄÉÍÏ ÕËÁÚÁÔØ: \verb'y=sawtooth(x,a)'. ôÁËÉÍ ÏÂÒÁÚÏÍ, ÞÔÏÂÙ ÐÏÌÕÞÉÔØ
|
||
<<ÐÉÌÕ>> Ó ÉÎÔÅÒ×ÁÌÏÍ ÓÉÇÎÁÌÁ × $[0,1]$ É ÐÅÒÉÏÄÏÍ~10, ÎÅÏÂÈÏÄÉÍÏ ÄÁÔØ ËÏÍÁÎÄÕ
|
||
\verb'y1=0.5+sawtooth(x*2*pi/10)/2;'. óÌÅÄÏ×ÁÔÅÌØÎÏ, ÐÏÌÕÞÉÔØ ÎÁÛ ÓÉÇÎÁÌ ÍÏÖÎÏ
|
||
ËÏÍÁÎÄÏÊ
|
||
$$\verb'y=sin(x*10).*(0.5+sawtooth(x*pi/5)/2);'$$
|
||
(ÎÅ ÚÁÂÕÄØÔÅ ÐÒÏ ÔÏÞËÕ ÐÅÒÅÄ ÚÎÁËÏÍ ÕÍÎÏÖÅÎÉÑ ÍÅÖÄÕ ÆÕÎËÃÉÑÍÉ, ÉÎÁÞÅ
|
||
ÐÏÌÕÞÉÔÅ ÏÛÉÂËÕ, Ô.Ë. Octave ÐÏÐÙÔÁÅÔÓÑ ÐÅÒÅÍÎÏÖÉÔØ Ä×Á ×ÅËÔÏÒÁ--ÓÔÒÏËÉ).
|
||
|
||
\task{îÁ ÉÎÔÅÒ×ÁÌÅ $[0,20]$ ÓÏÚÄÁÔØ Ä×Å ÓÉÎÕÓÏÉÄÙ, ÓÄ×ÉÎÕÔÙÅ ÄÒÕÇ ÏÔÎÏÓÉÔÅÌØÎÏ ÄÒÕÇÁ ÎÁ 3~ÅÄÉÎÉÃÙ.
|
||
ðÒÉ ÐÏÍÏÝÉ ×ÚÁÉÍÎÏ-ËÏÒÒÅÌÑÃÉÏÎÎÏÊ ÆÕÎËÃÉÉ ÏÐÒÅÄÅÌÉÔØ ÜÔÏÔ ÓÄ×ÉÇ.}
|
||
|
||
\verb'x=[0:0.05:20];' \verb'y=sin(x);'
|
||
\verb'y1=sin(x+3);'
|
||
|
||
ðÏÐÒÏÂÕÅÍ ÏÐÒÅÄÅÌÉÔØ, ÎÁ ÓËÏÌØËÏ ÅÄÉÎÉà ÓÄ×ÉÎÕÔ ÐÅÒ×ÙÊ
|
||
ÓÉÇÎÁÌ ÏÔÎÏÓÉÔÅÌØÎÏ ×ÔÏÒÏÇÏ. äÌÑ ÜÔÏÇÏ ×ÏÓÐÏÌØÚÕÅÍÓÑ ËÏÒÒÅÌÑÃÉÏÎÎÏÊ ÆÕÎËÃÉÅÊ.
|
||
úÁÐÉÛÅÍ \verb'Corr=xcorr(y,y1);'. ëÏÒÒÅÌÑÃÉÏÎÎÁÑ ÆÕÎËÃÉÑ × ÄÁÎÎÏÍ ÓÌÕÞÁÅ ÉÍÅÅÔ
|
||
×Ä×ÏÅ ÂÏÌØÛÕÀ ÛÉÒÉÎÕ, ÞÅÍ ÉÓÈÏÄÎÁÑ, Ô.Ë. ÏÎÁ ÐÏÌÕÞÁÅÔÓÑ ÐÕÔÅÍ ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏÇÏ
|
||
ÓÄ×ÉÇÁ ×ÔÏÒÏÊ ÆÕÎËÃÉÉ ÏÔÎÏÓÉÔÅÌØÎÏ ÐÅÒ×ÏÊ. ðÏÜÔÏÍÕ ÐÏÓÔÒÏÉÍ ÇÒÁÆÉË ËÏÍÁÎÄÏÊ
|
||
\verb'plot([-20:0.05:20],Corr)'. ÷ÏÓÐÏÌØÚÏ×Á×ÛÉÓØ ÆÕÎËÃÉÅÊ Õ×ÅÌÉÞÅÎÉÑ ÍÏÖÎÏ
|
||
Õ×ÉÄÅÔØ, ÞÔÏ ÂÌÉÖÁÊÛÉÊ Ë ÎÕÌÀ ÍÁËÓÉÍÕÍ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÓÄ×ÉÇÕ ÏÄÎÏÊ ÆÕÎËÃÉÉ
|
||
ÏÔÎÏÓÉÔÅÌØÎÏ ÄÒÕÇÏÊ. ÷ ÎÁÛÅÍ ÓÌÕÞÁÅ ÓÉÇÎÁÌ ÂÙÌ ÐÅÒÉÏÄÉÞÅÓËÉÍ, ÐÏÜÔÏÍÕ ÐÒÉ
|
||
ÓÄ×ÉÇÁÈ ÎÁ ×ÅÌÉÞÉÎÙ, ÐÒÅ×ÙÛÁÀÝÉÅ ÐÏÌÏ×ÉÎÕ ÐÅÒÉÏÄÁ, ×ÏÚÎÉËÁÅÔ ÏÛÉÂËÁ, ËÒÁÔÎÁÑ
|
||
ÐÏÌÕÐÅÒÉÏÄÕ. üÔÏ ÎÅÏÂÈÏÄÉÍÏ ÕÞÉÔÙ×ÁÔØ × ÒÁÓÞÅÔÁÈ.
|
||
|
||
ðÏÍÅÎÑÅÍ ÓÄ×ÉÇ ÎÁ~0.2 É ÐÏÓÍÏÔÒÉÍ, ËÁË ÉÚÍÅÎÉÔÓÑ ÇÒÁÆÉË.
|
||
|
||
\task{îÁÊÄÉÔÅ ÓÕÍÍÕ, ÒÁÚÎÏÓÔØ, ÐÒÏÉÚ×ÅÄÅÎÉÅ É ÞÁÓÔÎÏÅ ÍÁÔÒÉÃ
|
||
$$A=\begin{pmatrix}4&12&8\\7&11&-1\\2&12&3\end{pmatrix},\qquad
|
||
B=\begin{pmatrix}11&2&0\\0&3&0\\1&-1&12\end{pmatrix}.$$
|
||
îÁÊÄÉÔÅ ÏÐÒÅÄÅÌÉÔÅÌÉ ÉÓÈÏÄÎÙÈ É ÐÏÌÕÞÉ×ÛÉÈÓÑ ÍÁÔÒÉà (ËÏÍÁÎÄÁ \t{det(A)})}
|
||
\begin{verbatim}
|
||
a=[4 12 8; 7 11 -1; 2 12 3];
|
||
b=[11 2 0; 0 3 0; 1 -1 12];
|
||
sum=a+b
|
||
dif=a-b
|
||
prod=a*b
|
||
div=a/b
|
||
det(a) ...
|
||
\end{verbatim}
|
||
|
||
\section{úÁÄÁÎÉÑ ÄÌÑ ÓÁÍÏÓÔÏÑÔÅÌØÎÏÇÏ ×ÙÐÏÌÎÅÎÉÑ}
|
||
\begin{enumerate}
|
||
\item îÁÊÄÉÔÅ ÓÕÍÍÕ, ÒÁÚÎÏÓÔØ, ÐÒÏÉÚ×ÅÄÅÎÉÅ É ÞÁÓÔÎÏÅ ÍÁÔÒÉÃ
|
||
$$A=\begin{pmatrix}1&2&3\\6&5&4\\9&8&7\end{pmatrix},\qquad
|
||
B=\begin{pmatrix}9&8&7\\5&3&1\\0&2&6\end{pmatrix}.$$
|
||
îÁÊÄÉÔÅ ÏÐÒÅÄÅÌÉÔÅÌÉ ÉÓÈÏÄÎÙÈ É ÐÏÌÕÞÉ×ÛÉÈÓÑ ÍÁÔÒÉà (ËÏÍÁÎÄÁ \verb'det(A)').
|
||
|
||
\item
|
||
îÁÊÄÉÔÅ ÚÎÁÞÅÎÉÅ ÐÏÞÌÅÎÎÏÇÏ, ÍÁÔÒÉÞÎÏÇÏ É ÓËÁÌÑÒÎÏÇÏ ÐÒÏÉÚ×ÅÄÅÎÉÊ ×ÅËÔÏÒÏ×
|
||
$a=(2,5,7)$ É $b=(11,13,17)$. óËÁÌÑÒÎÏÅ ÐÒÏÉÚ×ÅÄÅÎÉÅ ÎÁÊÄÉÔÅ Ä×ÕÍÑ ÓÐÏÓÏÂÁÍÉ:
|
||
ÐÕÔÅÍ ÐÅÒÅÍÎÏÖÅÎÉÑ ×ÅËÔÏÒÏ× É ÐÒÉ ÐÏÍÏÝÉ ÆÕÎËÃÉÉ \verb'dot(a,b)'.
|
||
îÁÊÄÉÔÅ ×ÅËÔÏÒÎÏÅ ÐÒÏÉÚ×ÅÄÅÎÉÅ $a\times b$ ÐÒÉ ÐÏÍÏÝÉ ÆÕÎËÃÉÉ
|
||
\verb'cross(a,b)'.
|
||
|
||
\item
|
||
ðÏÓÔÒÏÊÔÅ ÇÒÁÆÉË ÎÏÒÍÁÌØÎÏÇÏ ÒÁÓÐÒÅÄÅÌÅÎÉÑ ÎÁ ÉÎÔÅÒ×ÁÌÅ $[0,100]$ Ó ÍÁÔÅÍÁÔÉÞÅÓËÉÍ
|
||
ÏÖÉÄÁÎÉÅÍ~50 É ÄÉÓÐÅÒÓÉÅÊ~100.
|
||
|
||
\item
|
||
\label{noicy_AM}
|
||
ðÏÌÕÞÉÔÅ ÓÉÇÎÁÌ Ó ÁÍÐÌÉÔÕÄÎÏÊ ÍÏÄÕÌÑÃÉÅÊ (ÉÚ ÐÒÉÍÅÒÁ). äÏÂÁ×ØÔÅ Ë ÎÅÍÕ ÇÁÕÓÓÏ×
|
||
ÂÅÌÙÊ ÛÕÍ Ó SNR 100, 50, 10 É~1~Äâ. ðÏÓÔÒÏÊÔÅ ÏÔÄÅÌØÎÏ ÇÒÁÆÉËÉ ×ÓÅÈ
|
||
ÐÏÌÕÞÅÎÎÙÈ ÓÉÇÎÁÌÏ×. íÏÖÎÏ ÌÉ ÓÄÅÌÁÔØ ËÁËÏÊ-ÌÉÂÏ ×Ù×ÏÄ Ï ×ÉÄÅ ÓÉÇÎÁÌÁ ÐÒÉ
|
||
SNR=1? ëÁË ×Ù ÄÕÍÁÅÔÅ, ÍÏÖÎÏ ÌÉ ×ÏÓÓÔÁÎÏ×ÉÔØ ÉÚ ÎÅÇÏ ÉÓÈÏÄÎÙÊ ÓÉÇÎÁÌ?
|
||
|
||
\item
|
||
äÌÑ ÐÏÌÕÞÅÎÎÏÇÏ ÓÉÇÎÁÌÁ ÎÁÊÄÉÔÅ ÓÌÅÄÕÀÝÉÅ ÈÁÒÁËÔÅÒÉÓÔÉËÉ: ÍÁÔÅÍÁÔÉÞÅÓËÏÅ ÏÖÉÄÁÎÉÅ
|
||
(\verb'mean'), ÓÒÅÄÎÅÅ Ë×ÁÄÒÁÔÉÞÎÏÅ ÏÔËÌÏÎÅÎÉÅ (\verb'std'), ÍÅÄÉÁÎÕ (\verb'median')
|
||
É ÍÏÄÕ (\verb'mode'). îÁÊÄÉÔÅ ÁÎÁÌÏÇÉÞÎÙÅ ×ÅÌÉÞÉÎÙ ÄÌÑ ÒÁÚÎÏÓÔÉ ÍÅÖÄÕ ÚÁÛÕÍÌÅÎÎÙÍ
|
||
É ÏÒÉÇÉÎÁÌØÎÙÍ ÓÉÇÎÁÌÏÍ. óÒÁ×ÎÉÔÅ ÐÏÌÕÞÅÎÎÙÅ ×ÅÌÉÞÉÎÙ Ó ÔÅÏÒÅÔÉÞÅÓËÉÍÉ.
|
||
|
||
\item
|
||
ðÏÐÙÔÁÊÔÅÓØ ÏÐÒÅÄÅÌÉÔØ ÓÄ×ÉÇ Ä×ÕÈ ÓÉÎÕÓÏÉÄ (ÉÚ ÐÒÉÍÅÒÁ) ÐÒÉ ÚÁÛÕÍÌÅÎÉÉ:
|
||
\begin{itemize}
|
||
\item ÔÏÌØËÏ ÏÄÎÏÊ Ó ÕÒÏ×ÎÅÍ ÓÉÇÎÁÌ/ÛÕÍ 1~Äâ;
|
||
\item ÏÂÅÉÈ Ó ÕÒÏ×ÎÅÍ SNR=1~Äâ;
|
||
\item ÏÄÎÏÊ Ó ÕÒÏ×ÎÅÍ SNR=0.1~Äâ;
|
||
\item ÏÂÅÉÈ Ó ÕÒÏ×ÎÅÍ SNR=0.1~Äâ.
|
||
\end{itemize}
|
||
ðÏÓÔÒÏÊÔÅ ÏÄÉÎ ÉÚ ÓÉÇÎÁÌÏ× Ó SNR=0.1~Äâ. íÏÖÎÏ ÌÉ ÏÐÒÅÄÅÌÉÔØ ÅÇÏ ÐÅÒÉÏÄ?
|
||
íÏÖÎÏ ÌÉ ÏÐÒÅÄÅÌÉÔØ ÐÅÒÉÏÄ ÐÏ Á×ÔÏËÏÒÒÅÌÑÃÉÏÎÎÏÊ ÆÕÎËÃÉÉ ÜÔÏÇÏ ÓÉÇÎÁÌÁ?
|
||
\end{enumerate}
|
||
|
||
|
||
\end{document}
|
||
|