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Файл:Теория информации. Лабораторный практикум в MATLAB. Учебное пособие
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ɇɟɩɪɟɪɵɜɧɵɟ ɢɫɬɨɱɧɢɤɢ ɢɧɮɨɪɦɚɰɢɢ
O
H[S
fu u m
O
ɫɦɚɬɟɦɚɬɢɱɟɫɤɢɦɨɠɢɞɚɧɢɟɦ
V
U
ɢɞɢɫɩɟɪɫɢɟɣ
m
U
O
U
O!
ɫɨɫɬɚɜɥɹɟɬ
e
ORJ ORJ
hU e
§·
V
¨¸
©¹
O
U
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɪɚɫ
ɩɪɟɞɟɥɟɧɧɨɣɩɨɪɚɜɧɨɦɟɪɧɨɦɭɡɚɤɨɧɭ
fu
°
ED
®
°
ɩɪɢ
¯
Dd dE
ɩɪɢ
u
D !E
uu
ɫɦɚɬɟɦɚɬɢɱɟɫɤɢɦɨɠɢɞɚɧɢɟɦɢɞɢɫɩɟɪɫɢɟɣ
m
DE
U
V
U
ED
ɫɨɫɬɚɜɥɹɟɬ
ORJ ORJ
hU ED V
U
Ⱦɨɤɚɡɚɧɨ ɱɬɨ ɟɫɥɢ ɟɞɢɧɫɬɜɟɧɧɵɦ ɨɝɪɚɧɢɱɟɧɢɟɦ ɞɥɹ ɫɥɭ
ɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ U ɹɜɥɹɟɬɫɹ ɨɛɥɚɫɬɶ ɟɟ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ
ɬɨɦɚɤɫɢɦɚɥɶɧɨɜɨɡɦɨɠɧɨɣɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣɷɧɬɪɨɩɢɟɣ
>@DE
ɨɩɪɟɞɟɥɹɟɦɨɣ ɪɚɜɟɧɫɬɜɨɦ ɨɛɥɚɞɚɟɬɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚɫ
ɪɚɜɧɨɦɟɪɧɵɦɪɚɫɩɪɟɞɟɥɟɧɢɟɦɜɟɪɨɹɬɧɨɫɬɟɣ
ɉɨɚɧɚɥɨɝɢɢɫɞɢɫɤɪɟɬɧɵɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɞɥɹ ɧɟɩɪɟɪɵɜɧɵɯ
ɢɫɬɨɱɧɢɤɨɜɬɚɤɠɟɜɜɨɞɹɬɫɹɩɨɧɹɬɢɹɫɨɜɦɟɫɬɧɨɣɢɭɫɥɨɜɧɨɣɞɢɮ
ɮɟɪɟɧɰɢɚɥɶɧɵɯ ɷɧɬɪɨɩɢɣ ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɹɸɬ ɭɱɢɬɵɜɚɬɶ ɫɬɚɬɢ
ɫɬɢɱɟɫɤɢɟ ɫɜɹɡɢ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢɫɢɝɧɚɥɨɜ U ɢ V ɞɜɭɯ ɢɥɢ ɧɟ
ɫɤɨɥɶɤɢɯɢɫɬɨɱɧɢɤɨɜɦɟɠɞɭɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦɢɫɟɱɟɧɢɹɦɢɫɢɝ
ɧɚɥɚɧɚɜɵɯɨɞɟɨɞɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɦɟɠɞɭ ɨɬɫɱɟɬɚɦɢ ɫɢɝɧɚɥɨɜ ɧɚ
ɜɯɨɞɟɢɜɵɯɨɞɟɤɚɧɚɥɚɫɜɹɡɢ
ɋɨɜɦɟɫɬɧɚɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹɷɧɬɪɨɩɢɹ ɞɜɭɯɫɟɱɟɧɢɣ U ɢ
V ɨɩɪɟɞɟɥɹɟɬɫɹɜɵɪɚɠɟɧɢɟɦ
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 6
ff
ɝɞɟ
fuv
ORJ h U V f u v f u v dudv
³³
f f
±ɫɨɜɦɟɫɬɧɚɹɩɥɨɬɧɨɫɬɶɪɚɫɩɪɟɞɟɥɟɧɢɹɫɥɭɱɚɣɧɵɯɜɟ
ɥɢɱɢɧUɢV
ɋɨɜɦɟɫɬɧɭɸ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɦɨɠɧɨ ɩɪɟɞ
fuv
ɫɬɚɜɢɬɶɜɜɢɞɟ
_ _ fuv fufvu fvfuv
ɝɞɟ
f
fu fuvdv
³
f
± ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɨɫɬɚɜɥɹɸɳɢɯ U ɢ V
f
fv fuvdu
³
f
_fuv
±
ɭɫɥɨɜɧɚɹɩɥɨɬɧɨɫɬɶɜɟɪɨɹɬɧɨɫɬɟɣɫɨɫɬɚɜɥɹɸɳɟɣUɩɪɢɡɚɞɚɧɧɨɦ
ɡɧɚɱɟɧɢɢ
Vv
ɫɬɚɜɥɹɸɳɟɣVɩɪɢɡɚɞɚɧɧɨɦɡɧɚɱɟɧɢɢ
_fvu
±ɭɫɥɨɜɧɚɹ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɨ
Uu
ɍɫɥɨɜɧɚɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹɷɧɬɪɨɩɢɹɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɵ
UɩɪɢɢɡɜɟɫɬɧɨɣɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɟVɨɩɪɟɞɟɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
ff
_ ORJ_h U V f u v f u v dudv
³³
f f
ɚ ɭɫɥɨɜɧɚɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ V
ɩɪɢɢɡɜɟɫɬɧɨɣɫɥɭɱɚɣɧɨɣɜɟɥɢɱɢɧɟUɫɨɫɬɚɜɥɹɟɬ
ff
_ ORJ_h V U f u v f v u dudv
³³
f f
ɂɡ ɜɵɪɚɠɟɧɢɣ ± ɫɥɟɞɭɟɬ ɱɬɨ ɩɟɪɟɱɢɫɥɟɧɧɵɟ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟɷɧɬɪɨɩɢɢɫɜɹɡɚɧɵɫɨɨɬɧɨɲɟɧɢɹɦɢ
_ hUV hV hU V
_ hU V hU hV U
ɩɪɢɱɟɦ ɞɥɹ ɫɬɚɬɢɫɬɢɱɟɫɤɢ ɧɟɡɚɜɢɫɢɦɵɯ ɫɟɱɟɧɢɣ U ɢ V ɤɨɝɞɚ ɜ
ɜɵɪɚɠɟɧɢɹɯɫɨɜɦɟɫɬɧɚɹɢɭɫɥɨɜɧɵɟɩɥɨɬɧɨɫɬɢɪɚɫɩɪɟɞɟɥɟ
ɧɢɹ
fuv fufv
ɢ
_ fuv fu
_ fvu fv
ɞɢɮɮɟ
ɇɟɩɪɟɪɵɜɧɵɟ ɢɫɬɨɱɧɢɤɢ ɢɧɮɨɪɦɚɰɢɢ
ɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɨɛɴɟɞɢɧɟɧɢɹ ɪɚɜɧɚ ɫɭɦɦɟɷɧɬɪɨɩɢɣ
hV
ɢ
hUV hU hV
hU
ɚ ɭɫɥɨɜɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɷɧɬɪɨɩɢɢ ɪɚɜɧɵ ɫɨɨɬɜɟɬɫɬɜɭɸ
ɳɢɦɛɟɡɭɫɥɨɜɧɵɦ
_ hU V hU
ɋɨɜɦɟɫɬɧɚɹ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɟɱɟɧɢɣ
ɫɬɚɰɢɨɧɚɪɧɨɝɨɝɚɭɫɫɨɜɫɤɨɝɨɫɢɝɧɚɥɚ
UUt
ɱɟɫɤɢɦ ɨɠɢɞɚɧɢɟɦ
ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɮɭɧɤɰɢɟɣ
ttW
ɨɩɪɟɞɟɥɹɟɬɫɹɜɵɪɚɠɟɧɢɟɦ
fu u
½
um r umu m um
W
°°
u
H[S
®¾
°°
¯¿
UU U U U
ɞɢɫɩɟɪɫɢɟɣ
m
U
r
U
W u
VW
_ hV U hV
ɢ ɧɨɪɦɢɪɨɜɚɧɧɨɣ ɚɜɬɨ
V
U
ɫɨɝɥɚɫɧɨ ɩɪɢ m ɢ
W
Ut
ɫɦɚɬɟɦɚɬɢ
SV W
UU
ªº
UU
¬¼
r
r
UUt
ɉɨɞɫɬɚɧɨɜɤɚ ɜ ɩɨɤɚɡɵɜɚɟɬ ɱɬɨ ɫɨɜɦɟɫɬɧɚɹ
ɢ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹɷɧɬɪɨɩɢɹɫɟɱɟɧɢɣ
U
U
ɪɚɜɧɚ
ɢ
ORJ
hU U e r
ªº
SWV
«»
¬¼
UU
ɚ ɭɫɥɨɜɧɚɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹɷɧɬɪɨɩɢɹɫɨɝɥɚɫɧɨ ɢ
ɫɨɫɬɚɜɥɹɟɬ
_ _ORJ
hU U hU U e r
SWV
^`
ªº
UU
¬¼
ORJ
SWV
er
^`
ªº
UU
¬¼
Ɋɚɫɱɟɬɧɵɟɡɚɞɚɧɢɹ
Ɂɚɞɚɧɢɟ ɂɫɩɨɥɶɡɭɹɮɨɪɦɭɥɵ
ɩɨɫɬɪɨɢɬɶɝɪɚɮɢɤɢɩɥɨɬɧɨɫɬɟɣɜɟɪɨɹɬɧɨɫɬɟɣ
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 6
ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ Uɪɚɫɩɪɟɞɟɥɟɧɧɵɯɩɨ ɡɚɤɨɧɭ Ƚɚɭɫɫɚ ɋɢɦɩ
ɫɨɧɚ Ʌɚɩɥɚɫɚ ɢ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɡɚɤɨɧɨɦ ɩɪɢ
m
U
ɢ
V
U
ȼɵɱɢɫɥɢɬɶ ɞɢɫɩɟɪɫɢɢ ɩɨɫɬɪɨɟɧɧɵɯ ɩɥɨɬɧɨɫɬɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɜɟɪɨɹɬɧɨɫɬɟɣ
%Script_6_1
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ ɩɥɨɬɧɨɫɬɟɣ ɜɟɪɨɹɬɧɨɫɬɟɣ
ɧɟɩɪɟɪɵɜɧɵɯ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ
%ɢ ɜɵɱɢɫɥɟɧɢɟ ɢɯ ɞɢɫɩɟɪɫɢɣ
clear all; close all; clc
%Ɂɚɞɚɧɢɟ ɚɧɨɧɢɦɧɵɯ ɮɭɧɤɰɢɣ ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ
Gauss=@(u)pdf('Normal',u,0,1);
Simpson=@(u)tripuls(u,2*sqrt(6))/sqrt(6);
Laplace=@(u)sqrt(2)/2*exp(-abs(u)*sqrt(2));
Uniform=@(u).5*rectpuls(u,2*sqrt(3))/sqrt(3);
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɚ
u=-4:.01:4;
%ȼɵɱɢɫɥɟɧɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɜɟɪɨɹɬɧɨɫɬɟɣ
f_G=Gauss(u);
f_S=Simpson(u);
f_L=Laplace(u);
f_U=Uniform(u);
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ
plot(u,f_G,u,f_S,u,f_L,u,f_U)
grid
xlabel('Ɂɧɚɱɟɧɢɹ ɚɪɝɭɦɟɧɬɚ u')
ylabel('ɉɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ f(u)')
title('Ɂɚɤɨɧɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ')
legend('Ƚɚɭɫɫɚ','ɋɢɦɩɫɨɧɚ','Ʌɚɩɥɚɫɚ','Ɋɚɜɧɨɦɟɪɧɵɣ')
%Ɂɚɞɚɧɢɟ ɚɧɨɧɢɦɧɵɯ ɮɭɧɤɰɢɣ
d_Gauss=@(u) u.^2.*Gauss(u);
d_Simpson=@(u) u.^2.*Simpson(u);
d_Laplace=@(u) u.^2.*Laplace(u);
d_Uniform=@(u) u.^2.*Uniform(u);
%ȼɵɱɢɫɥɟɧɢɟ ɞɢɫɩɟɪɫɢɣ
disp('Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɞɢɫɩɟɪɫɢɣ:')
disp('-----------------------------')
d_G=integral(d_Gauss,-Inf,Inf);
disp('Ɋɚɫɩɪɟɞɟɥɟɧɢɟ Ƚɚɭɫɫɚ:')
disp(d_G)
d_S=integral(d_Simpson,-Inf,Inf);
ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɞɢɫɩɟɪɫɢɣ
ɇɟɩɪɟɪɵɜɧɵɟ ɢɫɬɨɱɧɢɤɢ ɢɧɮɨɪɦɚɰɢɢ
disp('Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɋɢɦɩɫɨɧɚ:')
disp(d_S)
d_L=integral(d_Laplace,-Inf,Inf);
disp('Ɋɚɫɩɪɟɞɟɥɟɧɢɟ Ʌɚɩɥɚɫɚ:')
disp(d_L)
d_U=integral(d_Uniform,-Inf,Inf);
disp('Ɋɚɜɧɨɦɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ:')
disp(d_U)
Ɂɚɞɚɧɢɟ ɉɨ ɮɨɪɦɭɥɚɦ ɢ ɩɨ
ɫɬɪɨɢɬɶɝɪɚɮɢɤɢɡɚɜɢɫɢɦɨɫɬɟɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣɷɧɬɪɨɩɢɢɫɥɭ
ɱɚɣɧɵɯɜɟɥɢɱɢɧ UɪɚɫɩɪɟɞɟɥɟɧɧɵɯɩɨɡɚɤɨɧɭȽɚɭɫɫɚɋɢɦɩɫɨɧɚ
Ʌɚɩɥɚɫɚ ɢ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɡɚɤɨɧɨɦ ɨɬ ɜɟɥɢɱɢɧɵ ɞɢɫɩɟɪɫɢɢ
V
U
ɜɵɪɚɠɟɧɧɨɣɜɞɟɰɢɛɟɥɚɯ
%Script_6_2
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ ɡɚɜɢɫɢɦɨɫɬɟɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ
ɷɧɬɪɨɩɢɢ ɨɬ ɞɢɫɩɟɪɫɢɢ
clear all; close all; clc
e=exp(1);
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ ɞɢɫɩɟɪɫɢɢ ɜ ɞɟɰɢɛɟɥɚɯ
s_dB=0:.01:10;
%ȼɵɱɢɫɥɟɧɢɟ ɡɧɚɱɟɧɢɣ ɞɢɫɩɟɪɫɢɢ ɜ «ɪɚɡɚɯ»
s=10.^(.1*s_dB);
%ȼɵɱɢɫɥɟɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɷɧɬɪɨɩɢɣ
h_Gauss=.5*log2(2*pi*e*s);
h_Simpson=.5*log2(6*e*s);
h_Laplace=.5*log2(2*e^2*s);
h_Uniform=.5*log2(12*s);
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ
plot(s_dB,h_Gauss,s_dB,h_Simpson,s_dB,h_Laplace,s_dB,
h_Uniform)
grid
xlabel('Ⱦɢɫɩɟɪɫɢɹ \sigma^2_U, ɞȻ')
ylabel('Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ h(U), ɛɢɬ/ɨɬɫɱɟɬ')
str1='Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ';
str2='ɫ ɪɚɡɥɢɱɧɵɦɢ ɡɚɤɨɧɚɦɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɜɟɪɨɹɬɧɨɫɬɟɣ';
title({str1;str2})
legend('Ƚɚɭɫɫɚ','ɋɢɦɩɫɨɧɚ','Ʌɚɩɥɚɫɚ','Ɋɚɜɧɨɦɟɪɧɵɣ
'Location','Best')
',
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 6
Ɂɚɞɚɧɢɟ ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɮɨɪɦɭɥɵ ɩɨɫɬɪɨɢɬɶ
ɝɪɚɮɢɤɢ ɞɜɭɦɟɪɧɨɣ ɝɚɭɫɫɨɜɫɤɨɣ ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨ
ɹɬɧɨɫɬɟɣ ɢ ɥɢɧɢɢɭɪɨɜɧɹ ɩɪɢ
ɮɢɰɢɟɧɬɚɤɨɪɪɟɥɹɰɢɢ ±
%Script_6_3
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ ɩɥɨɬɧɨɫɬɢ ɞɜɭɦɟɪɧɨɝɨ ɧɨɪɦɚɥɶɧɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɥɢɧɢɣ
%ɭɪɨɜɧɹ ɩɪɢ ɧɭɥɟɜɨɦ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɨɠɢɞɚɧɢɢ,
ɟɞɢɧɢɱɧɨɣ ɞɢɫɩɟɪɫɢɢ
%ɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɤɨɷɮɮɢɰɢɟɧɬɚ ɤɨɪɪɟɥɹɰɢɢ
clear all; close all; clc
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɨɜ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɨɜ
umi=-2; uma=-umi;
du=.2;
u1=umi:du:uma;
u2=u1;
%Ɏɨɪɦɢɪɨɜɚɧɢɟ ɫɟɬɤɢ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɨɜ
[u1,u2]=meshgrid(u1,u2);
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ r
vr=[-.5 0 .5 .8];
%Ɉɩɪɟɞɟɥɟɧɢɟ ɞɥɢɧɵ ɜɟɤɬɨɪɚ
nr=length(vr);
%Ɂɚɞɚɧɢɟ ɪɚɡɦɟɪɧɨɫɬɢ ɦɚɫɫɢɜɚ
str=cell(1,nr);
%Ɋɚɫɱɟɬ ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
for k=1:nr
r=vr(k);
str{k}=['r_U = ',num2str(r)];
c=1/(2*pi*sqrt(1-r^2));
d=2*(1-r^2);
f=c*exp(-(u1.^2-2*r*u1.*u2+u2.^2)/d);
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ
subplot(2,2,k)
surf(u1,u2,f)
title(str(k))
xlabel('u_1')
ylabel('u_2')
zlabel('f(u_1,u_2)')
end
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɨɜ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɥɢɧɢɣ
ɭɪɨɜɧɹ
rr W
UU
m
U
ɢɡɧɚɱɟɧɢɹɯ ɤɨɷɮ
V
U
ɇɟɩɪɟɪɵɜɧɵɟ ɢɫɬɨɱɧɢɤɢ ɢɧɮɨɪɦɚɰɢɢ
du=.01;
u1=umi:du:uma;
u2=u1;
%Ɏɨɪɦɢɪɨɜɚɧɢɟ ɫɟɬɤɢ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɨɜ
[u1,u2]=meshgrid(u1,u2);
figure
%Ɋɚɫɱɟɬ ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
for k=1:nr
r=vr(k);
c=1/(2*pi*sqrt(1-r^2));
d=2*(1-r^2);
f=c*exp(-(u1.^2-2*r*u1.*u2+u2.^2)/d);
subplot(2,2,k)
%ɉɨɫɬɪɨɟɧɢɟ ɥɢɧɢɣ ɭɪɨɜɧɹ
contour(u1,u2,f)
grid
colorbar
title(str(k))
xlabel('u_1')
ylabel('u_2')
end
Ɂɚɞɚɧɢɟ ɉɨ ɮɨɪɦɭɥɟ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢ
ɦɨɫɬɟɣɭɫɥɨɜɧɨɣɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣɷɧɬɪɨɩɢɢɫɟɱɟɧɢɣ
ɢ
ɜɟɥɢɱɢɧɵɞɢɫɩɟɪɫɢɢ
ɹɯɤɨɷɮɮɢɰɢɟɧɬɚɤɨɪɪɟɥɹɰɢɢ
ɫɬɚɰɢɨɧɚɪɧɨɝɨɝɚɭɫɫɨɜɫɤɨɝɨɫɥɭɱɚɣɧɨɝɨɩɪɨɰɟɫɫɚɨɬ
UUt
ɜɵɪɚɠɟɧɧɨɣɜɞɟɰɢɛɟɥɚɯɩɪɢɡɧɚɱɟɧɢ
V
U
rr W
UU
UUt
%Script_6_4
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ ɡɚɜɢɫɢɦɨɫɬɟɣ ɭɫɥɨɜɧɨɣ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧɬɪɨɩɢɢ
%ɫɟɱɟɧɢɣ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɝɚɭɫɫɨɜɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɨɬ
ɞɢɫɩɟɪɫɢɢ
%ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɤɨɷɮɮɢɰɢɟɧɬɚ ɤɨɪɪɟɥɹɰɢɢ
clear all; close all; clc
e=exp(1);
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ ɞɢɫɩɟɪɫɢɢ ɜ ɞɟɰɢɛɟɥɚɯ
s_dB=0:.01:10;
%ȼɵɱɢɫɥɟɧɢɟ ɡɧɚɱɟɧɢɣ ɞɢɫɩɟɪɫɢɢ ɜ «ɪɚɡɚɯ»
s=10.^(.1*s_dB);
%Ɂɚɞɚɧɢɟ ɡɧɚɱɟɧɢɣ r
Ʌɚɛɨɪɚɬɨɪɧɚɹ ɪɚɛɨɬɚ ʋ 6
vr=[0 .5 .9 .99];
%Ɉɩɪɟɞɟɥɟɧɢɟ ɞɥɢɧɵ ɜɟɤɬɨɪɨɜ
ns=length(s);
nr=length(vr);
%Ɂɚɞɚɧɢɟ ɪɚɡɦɟɪɧɨɫɬɟɣ ɦɚɫɫɢɜɨɜ
h=zeros(nr,ns);
str=cell(1,nr);
%ȼɵɱɢɫɥɟɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɷɧɬɪɨɩɢɣ
for k=1:nr
r=vr(k);
str{k}=['r_U = ',num2str(r)];
h(k,:)=.5*log2(2*pi*e*sqrt(1-r^2)*s);
end
%ɉɨɫɬɪɨɟɧɢɟ ɝɪɚɮɢɤɨɜ
plot(s_dB,h)
grid
xlabel('\sigma^2_U, ɞȻ')
ylabel('h(U_1|U_2), ɛɢɬ/ɨɬɫɱɟɬ')
legend(str,'Location','NorthWest')
str1='ɍɫɥɨɜɧɚɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɫɟɱɟɧɢɣ
ɝɚɭɫɫɨɜɫɤɨɝɨ ɩɪɨɰɟɫɫɚ';
str2='ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɤɨɪɪɟɥɹɰɢɢ';
title({str1;str2})
Ɉɬɱɟɬɢɤɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ
Ɉɬɱɟɬɩɨɥɚɛɨɪɚɬɨɪɧɨɣɪɚɛɨɬɟɨɮɨɪɦɥɹɟɬɫɹɜɜɢɞɟɞɨɤɭɦɟɧ
ɬɚ06:RUGɢɞɨɥɠɟɧɫɨɞɟɪɠɚɬɶ
ɇɚɡɜɚɧɢɟ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɵ ɲɪɢɮɬ 7LPHV 1HZ
5RPDQ
Ɋɟɡɭɥɶɬɚɬɵɜɵɩɨɥɧɟɧɢɹɜɫɟɯɪɚɫɱɟɬɧɵɯɡɚɞɚɧɢɣɜɤɥɸɱɚɹ
ɥɢɫɬɢɧɝɢ Pɮɚɣɥɨɜ ɤɨɩɢɪɭɟɦɵɟ ɢɡ ɨɤɧɚ (GLWRU ɪɟɡɭɥɶɬɚɬɵ ɢɯ
ɜɵɩɨɥɧɟɧɢɹ ɤɨɩɢɪɭɟɦɵɟ ɢɡ ɨɤɧɚ &RPPDQG :LQGRZ ɲɪɢɮɬ
&RXULHU1HZɚɬɚɤɠɟɩɨɥɭɱɟɧɧɵɟɝɪɚɮɢɤɢ ɤɨɩɢɪɭɟɦɵɟ ɢɡ ɨɤɧɚ
)LJXUHɩɨɤɨɦɚɧɞɟ(GLW_&RS\)LJXUH
Ɂɚɳɢɬɚ ɥɚɛɨɪɚɬɨɪɧɨɣ ɪɚɛɨɬɵ ɩɪɨɜɨɞɢɬɫɹ ɧɚ ɨɫɧɨɜɟ ɩɪɟɞ
ɫɬɚɜɥɟɧɧɨɝɨɨɬɱɟɬɚɢɨɬɜɟɬɨɜɧɚɤɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ ɢɡ ɫɥɟɞɭ
ɸɳɟɝɨɫɩɢɫɤɚ
Ⱦɚɣɬɟɨɩɪɟɞɟɥɟɧɢɟɧɟɩɪɟɪɵɜɧɨɝɨɢɫɬɨɱɧɢɤɚɢɧɮɨɪɦɚɰɢɢ
ɇɟɩɪɟɪɵɜɧɵɟ ɢɫɬɨɱɧɢɤɢ ɢɧɮɨɪɦɚɰɢɢ
ɑɬɨɬɚɤɨɟɫɟɱɟɧɢɟɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ" ɗɬɨɞɟɬɟɪɦɢɧɢɪɨ
ɜɚɧɧɚɹɢɥɢɫɥɭɱɚɣɧɚɹɜɟɥɢɱɢɧɚ"
ɑɬɨ ɬɚɤɨɟ ɪɟɚɥɢɡɚɰɢɹ ɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ" ɗɬɨɞɟɬɟɪɦɢ
ɧɢɪɨɜɚɧɧɚɹɢɥɢɫɥɭɱɚɣɧɚɹɮɭɧɤɰɢɹ"
Ʉɚɤɢɦɨɛɪɚɡɨɦɨɩɢɫɵɜɚɟɬɫɹɫɥɭɱɚɣɧɵɣɫɢɝɧɚɥ"
Ⱦɚɣɬɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɜ ɭɡɤɨɦ ɫɦɵɫɥɟ ɫɥɭ
ɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
Ʉɚɤɨɣ ɜɢɞ ɢɦɟɸɬ ɨɞɧɨɦɟɪɧɚɹ ɞɜɭɦɟɪɧɚɹ ɢ mɦɟɪɧɚɹ
ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɜ ɭɡɤɨɦ
ɫɦɵɫɥɟɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ"
Ⱦɚɣɬɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɜ ɲɢɪɨɤɨɦ ɫɦɵɫɥɟ
ɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
Ɂɚɩɢɲɢɬɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɠɢɞɚɧɢɹ ɢ
ɞɢɫɩɟɪɫɢɢɫɬɚɰɢɨɧɚɪɧɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
Ɂɚɩɢɲɢɬɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɚɜɬɨɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɮɭɧɤɰɢɢ
ɫɬɚɰɢɨɧɚɪɧɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚɢɩɟɪɟɱɢɫɥɢɬɟɟɟɫɜɨɣɫɬɜɚ
Ⱦɚɣɬɟɨɩɪɟɞɟɥɟɧɢɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɫɩɟɤɬɪɚ ɫɩɟɤɬɪɚɥɶ
ɧɨɣ ɩɥɨɬɧɨɫɬɢ ɦɨɳɧɨɫɬɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɥɭɱɚɣɧɨɝɨ ɫɢɝɧɚɥɚ ɢ
ɩɟɪɟɱɢɫɥɢɬɟɟɝɨɫɜɨɣɫɬɜɚ
Ⱦɚɣɬɟɨɩɪɟɞɟɥɟɧɢɟɷɪɝɨɞɢɱɟɫɤɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
ɑɬɨɬɚɤɨɟɝɚɭɫɫɨɜɫɤɢɣɧɨɪɦɚɥɶɧɵɣɫɥɭɱɚɣɧɵɣɫɢɝɧɚɥ"
Ɂɚɩɢɲɢɬɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɨɞɧɨɦɟɪɧɨɣ ɩɥɨɬɧɨɫɬɢ ɪɚɫ
ɩɪɟɞɟɥɟɧɢɹɝɚɭɫɫɨɜɫɤɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
ɉɪɢɜɟɞɢɬɟ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɟ ɷɪɝɨɞɢɱɧɨɫɬɢ ɝɚɭɫɫɨɜ
ɫɤɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
Ʉɚɤɨɣɧɟɩɪɟɪɵɜɧɵɣɢɫɬɨɱɧɢɤɧɚɡɵɜɚɟɬɫɹ ɫɬɚɰɢɨɧɚɪɧɵɦ
ɷɪɝɨɞɢɱɟɫɤɢɦɢɫɬɨɱɧɢɤɨɦɢɧɮɨɪɦɚɰɢɢ"
ɉɪɢɜɟɞɢɬɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧɬɪɨɩɢɢ
ɫɟɱɟɧɢɹɫɬɚɰɢɨɧɚɪɧɨɝɨɫɥɭɱɚɣɧɨɝɨɫɢɝɧɚɥɚ
ɉɟɪɟɱɢɫɥɢɬɟɫɜɨɣɫɬɜɚɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣɷɧɬɪɨɩɢɢ
ɑɟɦɭ ɪɚɜɧɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɫɟɱɟɧɢɹ ɝɚɭɫ
ɫɨɜɫɤɨɝɨ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɥɭɱɚɣɧɨɝɨ ɫɢɝɧɚɥɚ" Ʉɚɤɢɦ ɜɚɠɧɵɦ
ɫɜɨɣɫɬɜɨɦɨɧɚɨɛɥɚɞɚɟɬ"
Ⱦɚɣɬɟ ɨɩɪɟɞɟɥɟɧɢɟ ɫɨɜɦɟɫɬɧɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧ
ɬɪɨɩɢɢɞɜɭɯɫɟɱɟɧɢɣɫɬɚɰɢɨɧɚɪɧɵɯɫɥɭɱɚɣɧɵɯɫɢɝɧɚɥɨɜ
ɉɪɢɜɟɞɢɬɟ ɞɜɟ ɮɨɪɦɵ ɡɚɩɢɫɢ ɞɥɹ ɫɨɜɦɟɫɬɧɨɣ ɞɢɮɮɟ
ɪɟɧɰɢɚɥɶɧɨɣɷɧɬɪɨɩɢɢ
Ʌɚɛɨɪɚɬɨɪɧɚɹɪɚɛɨɬɚʋ
ɇɟɩɪɟɪɵɜɧɵɟɤɚɧɚɥɵɫɜɹɡɢ
ɐɟɥɶɪɚɛɨɬɵ ɂɡɭɱɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɧɟɩɪɟɪɵɜɧɵɯɤɚɧɚ
ɥɨɜ ɫɜɹɡɢ ɨɜɥɚɞɟɬɶ ɩɪɨɝɪɚɦɦɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɢɯ ɪɚɫɱɟɬɚ ɜ
0$7/$%
Ɍɟɨɪɟɬɢɱɟɫɤɢɟɫɜɟɞɟɧɢɹ
ɇɟɩɪɟɪɵɜɧɵɣɤɚɧɚɥɫɜɹɡɢ ± ɷɬɨ ɤɚɧɚɥɭɤɨɬɨɪɨɝɨɩɨɫɬɭɩɚ
ɸɳɢɟ ɧɚ ɟɝɨɜɯɨɞ ɢɫɧɢɦɚɟɦɵɟ ɫ ɟɝɨ ɜɵɯɨɞɚ ɫɢɝɧɚɥɵɹɜɥɹɸɬɫɹ
ɪɟɚɥɢɡɚɰɢɹɦɢɧɟɩɪɟɪɵɜɧɵɯɫɥɭɱɚɣɧɵɯɩɪɨɰɟɫɫɨɜ
Ɋɟɚɥɢɡɚɰɢɹ
st
ɫɥɭɱɚɣɧɨɝɨ ɫɢɝɧɚɥɚ
St
ɧɚ ɜɵɯɨɞɟ ɧɟɩɪɟ
ɪɵɜɧɨɝɨɤɚɧɚɥɚɫɜɹɡɢɨɩɪɟɞɟɥɹɟɬɫɹɜɵɪɚɠɟɧɢɟɦ
ut
ɝɞɟ
Ut
ɢ ɚɞɞɢɬɢɜɧɨɝɨɲɭɦɚ
ɢ
nt
st ut nt
± ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɟɚɥɢɡɚɰɢɢ ɩɨɥɟɡɧɨɝɨ ɫɢɝɧɚɥɚ
Nt
ɜɢɫɢɦɵɦɢɫɥɭɱɚɣɧɵɦɢɩɪɨɰɟɫɫɚɦɢ
tTdd
ɹɜɥɹɸɳɢɯɫɹɫɬɚɬɢɫɬɢɱɟɫɤɢɧɟɡɚ
T
±ɞɥɢɬɟɥɶɧɨɫɬɶɫɢɝɧɚɥɚ
ɇɟɩɪɟɪɵɜɧɵɣ ɤɚɧɚɥ ɫɜɹɡɢ ɨɩɢɫɵɜɚɟɦɵɣ ɦɨɞɟɥɶɸ
ɸɳɢɦɞɨɩɭɳɟɧɢɹɦ
±ɨɫɧɨɜɧɵɟɩɚɪɚɦɟɬɪɵɤɚɧɚɥɚ ɤɨɷɮɮɢɰɢɟɧɬɩɟɪɟɞɚɱɢɤɚɧɚ
ɥɚɢɡɚɞɟɪɠɤɚɫɢɝɧɚɥɚɹɜɥɹɸɬɫɹ ɢɡɜɟɫɬɧɵɦɢɩɨɫɬɨɹɧɧɵɦɢɜɟɥɢ
ɱɢɧɚɦɢ
±ɩɨɥɨɫɚ ɩɪɨɩɭɫɤɚɧɢɹ ɤɚɧɚɥɚ ɨɝɪɚɧɢɱɟɧɚ ɜɟɪɯɧɟɣ ɱɚɫɬɨɬɨɣ
F
±ɩɨɥɟɡɧɵɣɫɢɝɧɚɥ
Ut
ɹɜɥɹɟɬɫɹɫɬɚɰɢɨɧɚɪɧɵɦɫɥɭɱɚɣɧɵɦ
ɩɪɨɰɟɫɫɨɦ ɫ ɧɭɥɟɜɵɦ ɫɪɟɞɧɢɦ ɡɧɚɱɟɧɢɟɦ ɢ ɩɨɫɬɨɹɧɧɨɣ ɞɢɫɩɟɪ
ɫɢɟɣɫɪɟɞɧɟɣɦɨɳɧɨɫɬɶɸ
Nt
±ɲɭɦ
ɨɩɢɫɵɜɚɟɬɫɹɦɨɞɟɥɶɸɚɞɞɢɬɢɜɧɨɝɨɛɟɥɨɝɨɝɚɭɫ
UU
PV
ɫɨɜɫɤɨɝɨ ɲɭɦɚ ɫ ɨɞɧɨɫɬɨɪɨɧɧɟɣɫɩɟɤɬɪɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɦɨɳ
ɧɨɫɬɢ
N
Ƚɚɭɫɫɨɜɫɤɢɣ ɤɚɧɚɥ ɱɚɫɬɨɧɚɡɵɜɚɸɬɱɚɫɬɨɬɧɨɨɝɪɚɧɢɱɟɧɧɵɦ
ɤɚɧɚɥɨɦɫɩɨɫɬɨɹɧɧɵɦɢɩɚɪɚɦɟɬɪɚɦɢɢɚɞɞɢɬɢɜɧɵɦɛɟɥɵɦɝɚɭɫ
ɫɨɜɫɤɢɦɲɭɦɨɦ
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