Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 41 стр.

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Ɂɚɩɢɲɟɦ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɫ ɭɱɟɬɨɦ ɧɟɢɡɜɟɫɬɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ȼ
f(X,B) = f(X)f(X/B) = f(B)f(X/B). Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɟɣ ɡɚɩɢɫɚɧɵ
ɞɥɹ ɫɥɭɱɚɹ ɧɚɥɢɱɢɹ ɨɛɧɚɪɭɠɢɜɚɟɦɨɝɨ ɫɢɝɧɚɥɚ. ɉɨɞɟɥɢɦ ɨɛɟ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ ɧɚ
f(X/s
0
) ɢ ɩɪɨɢɧɬɟɝɪɢɪɭɟɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɨ ɦɧɨɠɟɫɬɜɭ ɧɟɢɡɜɟɫɬɧɵɯ
ɩɚɪɚɦɟɬɪɨɜ:
f(X/s
1
)/f(X/s
0
)=
³
:
B
(f(X/B)/f(X/s
0
))dB=¢l(X/B)²
B
.
Ɍɨ ɟɫɬɶ ɡɚɩɢɫɵɜɚɟɦ ɭɫɥɨɜɧɨɟ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɞɥɹ ɩɪɨɢɡɜɨɥɶɧɨɝɨ ɧɟ-
ɢɡɜɟɫɬɧɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɚ ɡɚɬɟɦ ɟɝɨ ɭɫɪɟɞɧɹɟɦ ɩɨ ɜɫɟɦ ɧɟɢɡɜɟɫɬɧɵɦ ɩɚɪɚɦɟɬɪɚɦ,
ɭɱɢɬɵɜɚɹ ɢɯ ɜɟɪɨɹɬɧɨɫɬɧɵɟ ɫɜɨɣɫɬɜɚ, ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɥɨɬɧɨɫɬɶɸ ɜɟɪɨɹɬɧɨɫɬɢ
f(B).
8.5.ɋɢɧɬɟɡ ɭɫɬɪɨɣɫɬɜɚ ɨɛɧɚɪɭɠɟɧɢɹ ɞɥɹ ɫɢɝɧɚɥɚ
ɫɨ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ
ɋɢɝɧɚɥ ɫ ɧɟɢɡɦɟɧɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɧɨ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɬɚɤɨɣ ɮɨɪɦɟ:
s(t,M)=s(t)cos[Z
0
t+I
s
(t)+M)], ɝɞɟ s(t)-ɫɨɦɧɨɠɢɬɟɥɶ,
ɨɩɪɟɞɟɥɹɸɳɢɣ ɮɨɪɦɭ ɫɢɝɧɚɥɚ;
Z
0
- ɮɢɤɫɢɪɨɜɚɧɧɚɹ ɱɚɫɬɨɬɚ; I
s
(t) - ɞɟɬɟɪɦɢɧɢɪɨ-
ɜɚɧɧɚɹ ɮɭɧɤɰɢɹ ɮɚɡɨɜɨɣ ɦɨɞɭɥɹɰɢɢ;
M - ɫɥɭɱɚɣɧɚɹ ɮɚɡɚ ɫ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ, ɪɚɜ-
ɧɨɦɟɪɧɵɦ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 0 ɞɨ 2
S.
ɉɪɟɨɛɪɚɡɭɟɦ ɤɨɫɢɧɭɫ ɫɭɦɦɵ ɜ ɜɵɪɚɠɟɧɢɢ ɞɥɹ ɫɢɝɧɚɥɚ ɩɨ ɢɡɜɟɫɬɧɨɣ ɮɨɪ-
ɦɭɥɟ ɢ ɩɨɥɭɱɢɦ
s(t,M) = s
c
(t)cos M - s
s
(t)sin M. ɉɨɞɫɬɚɜɢɦ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɜ
ɮɨɪɦɭɥɭ ɞɥɹ ɤɨɪɪɟɥɹɰɢɨɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ:
z(X/M) = z
c
cosM-z
s
sinM = Zcos(M-]), ɝɞɟ Z = (z
c
2
+z
s
2
)
1/2
, ]=
= arc
tg(z
s
/z
c
); z
c
=
³
T
0
s
c
(t)x(t)dt z
s
=
³
T
0
s
s
(t)x(t)dt. ȼɵɪɚɠɟɧɢɟ ɞɥɹ ɷɧɟɪɝɢɢ ɫɢɝɧɚɥɚ: E(M
)
=
³
T
0
s
2
(t)cos
2
[Z
0
t+I
s
(t)+M]dt|E ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɡɚɜɢɫɢɦɵɦ ɨɬ M, ɟɫɥɢ ɞɥɢɬɟɥɶ-
ɧɨɫɬɶ ɫɢɝɧɚɥɚ ɦɧɨɝɨ ɛɨɥɶɲɟ ɩɟɪɢɨɞɚ ɡɚɩɨɥɧɟɧɢɹ 1/
f
0
. Ɍɨɝɞɚ ɞɥɹ ɩɪɢɟɦɚ ɫɢɝɧɚɥɚ
ɧɚ ɮɨɧɟ ɧɨɪɦɚɥɶɧɨɝɨ ɲɭɦɚ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɨɬɧɨɲɟɧɢɟ ɩɪɚɜɞɨɩɨɞɨɛɢɹ ɜ ɬɚɤɨɦ
ɜɢɞɟ:
l
M
(X) = exp(-E/S
0
)(2S)
-1
³
S
2
0
exp[Zcos(M-])]dM = exp(-E/S
0
)I
0
(Z),
ɝɞɟ I
0
(x) - ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɚɹ ɮɭɧɤɰɢɹ Ȼɟɫɫɟɥɹ ɧɭɥɟɜɨɝɨ ɩɨɪɹɞɤɚ. ɗɬɚ ɮɭɧɤɰɢɹ
ɦɨɧɨɬɨɧɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɜɨɟɝɨ ɚɪɝɭɦɟɧɬɚ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɪɟɲɚɸɳɟɟ
ɩɪɚɜɢɥɨ:
Z t z
0
. ɋɬɪɭɤɬɭɪɚ ɨɩɬɢɦɚɥɶɧɨɝɨ ɩɪɢɟɦɧɨ-ɪɟɲɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɫɨ-
ɞɟɪɠɢɬ ɞɜɚ "ɤɜɚɞɪɚɬɭɪɧɵɯ" ɤɚɧɚɥɚ, ɤɜɚɞɪɚɬɨɪɵ ɜ ɤɚɠɞɨɦ ɢɡ ɧɢɯ, ɫɭɦɦɚɬɨɪ ɢ
ɩɨɪɨɝɨɜɨɟ ɭɫɬɪɨɣɫɬɜɨ. ɉɪɢ ɫɥɭɱɚɣɧɨɣ ɧɚɱɚɥɶɧɨɣ ɮɚɡɟ, ɟɫɥɢ ɫɢɝɧɚɥ ɧɟ ɫɨɡɞɚɟɬ

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