Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 60 стр.

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ɧɵɟ ɮɭɧɤɰɢɢ B
[
(t
1
,t
2
), B
K
(t
1
,t
2
) ɢ B
[K
(t
1
,t
2
) ɢɡɜɟɫɬɧɵ ɢ ɨɛɨɡɧɚɱɢɦ ɤɨɪɪɟɥɹɰɢɨɧ-
ɧɭɸ ɮɭɧɤɰɢɸ ɜɯɨɞɧɨɣ ɫɦɟɫɢ ɢ ɜɡɚɢɦɧɭɸ ɤɨɪɪɟɥɹɰɢɨɧɧɭɸ ɮɭɧɤɰɢɸ ɜɯɨɞɧɨɣ
ɫɦɟɫɢ ɢ ɲɭɦɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
B
x
(
t
1
,t
2
) ɢ B
x[
(t
1
,t
2
). Ɍɚɤ ɤɚɤ <x(u)x(v)> = B
x
(u,v) =
B
[
(u,v) + B
[
K(u,v) + B
K
[(u,v) + B
K
(u,v); <x(W)[(t)> = B
x
(u,v) = = B
[
(u,v) + B
[K
(u,v)
+
B
K[
(u,v) + B
K
(u,v); <x(W)[(t)> = B
x[
(W,t) = B
[
(W,t) + B
[K
(W,t), ɬɨ, ɩɨɞɫɬɚɜɢɜ ɷɬɢ ɜɵ-
ɪɚɠɟɧɢɹ ɜ ɮɨɪɦɭɥɭ ɞɥɹ
H
2
(t), ɧɚɯɨɞɢɦ
H
2
(t) = B
[
(t,t) -2
³
f
f
WW[W
t)d,()Bh(t,
x
+
³
f
f
³
f
f
h(t,u)h(t,v)B
x
(u,v)dudv.
ɂɡ ɷɬɨɣ ɮɨɪɦɭɥɵ ɫɥɟɞɭɟɬ, ɱɬɨ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɚɹ ɨɲɢɛɤɚ ɥɢɧɟɣɧɨɣ
ɨɰɟɧɤɢ
[(t) ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɢ ɜɡɚɢɦɧɨɣ ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ
ɮɭɧɤɰɢɣ ɩɪɨɰɟɫɫɨɜ
[(t) ɢ K(t) ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɛɨɥɟɟ ɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ ɷɬɢɯ ɩɪɨ-
ɰɟɫɫɨɜ.
Ⱦɨɤɚɠɟɦ, ɱɬɨ ɩɪɢ ɡɚɞɚɧɧɵɯ
B
[
, B
K
, B
[K
ɧɚɢɥɭɱɲɭɸ (ɜ ɫɦɵɫɥɟ ɩɪɢɧɹɬɨɝɨ
ɤɪɢɬɟɪɢɹ) ɥɢɧɟɣɧɭɸ ɮɢɥɶɬɪɚɰɢɸ ɩɪɨɰɟɫɫɚ
[(t) ɢɡ ɟɝɨ ɚɞɞɢɬɢɜɧɨɣ ɫɦɟɫɢ ɫ K(t)
ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶ ɥɢɧɟɣɧɚɹ ɫɢɫɬɟɦɚ, ɢɦɩɭɥɶɫɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɤɨɬɨɪɨɣ
ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɢɧɬɟɝɪɚɥɶɧɨɦɭ ɭɪɚɜɧɟɧɢɸ
B
x[
(W,t)=
³
f
f
h*(t,y)B
x
(W,y)dy. (14.2)
ɉɨɞɫɬɚɜɢɦ ɜɵɪɚɠɟɧɢɟ (14.2) ɜ ɮɨɪɦɭɥɭ ɞɥɹ
H
2
(t) ɢ ɩɨɤɚɠɟɦ, ɱɬɨ ɨɲɢɛɤɚ H
2
(t) ɦɢɧɢɦɚɥɶɧɚ ɩɪɢ ɭɫɥɨɜɢɢ h(t,W) = h*(t,W). ɇɚ ɫɚɦɨɦ ɞɟɥɟ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɭɤɚɡɚɧ-
ɧɨɣ ɜɵɲɟ ɩɨɞɫɬɚɧɨɜɤɢ ɩɨɥɭɱɢɦ
H
2
(t) = B
[
(t,t) -ҏ2
³
f
f
³
f
f
h(t,W)h*(t,y)B
x
(W,y)dWdy +
+
³
f
f
³
f
f
h(t,u)h(t,v)B
x
(u,v)dudv = B(t,t) -
-
³
f
f
³
f
f
h*(t,W)h*(t,y)B
x
(W,y)dWdy +
³
f
f
³
f
f
B
x
(u,v)[h(t,u) -
-ҏ
h*(t,u)][h(t,v) -ҏh*(t,v)]dudv.
Ɍɚɤ ɤɚɤ ɬɨɥɶɤɨ ɩɨɫɥɟɞɧɟɟ ɫɥɚɝɚɟɦɨɟ ɜ ɷɬɨɦ ɜɵɪɚɠɟɧɢɢ ɫɨɞɟɪɠɢɬ ɧɟɢɡɜɟɫɬ-
ɧɭɸ ɮɭɧɤɰɢɸ
h(t,u) ɢ ɬɚɤ ɤɚɤ ɷɬɨ ɫɥɚɝɚɟɦɨɟ ɧɟɨɬɪɢɰɚɬɟɥɶɧɨ (ɜ ɫɢɥɭ ɩɨɥɨɠɢɬɟɥɶ-
ɧɨɣ ɩɨɥɭɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɤɜɚɞɪɚɬɢɱɧɨɣ ɮɨɪɦɵ ɜ ɩɨɤɚɡɚɬɟɥɟ ɷɤɫɩɨɧɟɧɬɵ ɧɨɪ-
ɦɚɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɢ), ɬɨ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ
H
2
(t) ɛɭɞɟɬ ɫɨɨɬɜɟɬ-
ɫɬɜɨɜɚɬɶ ɬɚɤɨɣ ɥɢɧɟɣɧɨɣ ɫɢɫɬɟɦɟ, ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɤɨɬɨɪɨɣ ɨɛɪɚɳɚɟɬɫɹ ɜ
ɧɭɥɶ. Ⱥ ɷɬɨ ɛɭɞɟɬ ɢɦɟɬɶ ɦɟɫɬɨ ɩɪɢ ɭɫɥɨɜɢɢ
h(t,W) = h*(t,W), ɱɬɨ ɢ ɬɪɟɛɨɜɚɥɨɫɶ ɞɨ-
ɤɚɡɚɬɶ.

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