Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 49 стр.

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ɧɨɫɢɬɟɥɶɧɨ ɩɚɪɚɦɟɬɪɚ a. ȿɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɪɚɜɧɨ 2E/S
0
, ɬ.ɟ. ɩɪɢ a = a
0
,
ɤɨɝɞɚ ɩɚɪɚɦɟɬɪɵ ɨɩɨɪɧɨɝɨ ɫɢɝɧɚɥɚ ɢ ɢɫɫɥɟɞɭɟɦɨɝɨ ɫɢɝɧɚɥɚ ɫɨɜɩɚɞɚɸɬ, ɢɦɟɟɦ
(2/S
0
)
0
T
Ø
s
2
(t,a)dt = 2E/S
0
.
ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɲɭɦɨɜɨɣ ɮɭɧɤɰɢɢ ɪɚɜɧɨ ɧɭɥɸ, ɬɚɤ ɤɚɤ <[(t)>=0, ɚɫɪɟɞ-
ɧɟɟ ɡɧɚɱɟɧɢɟ ɤɜɚɞɪɚɬɚ ɷɬɨɣ ɮɭɧɤɰɢɢ ɟɫɬɶ 2ȿ/S
0
. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɲɭɦɨɜɚɹ ɮɭɧɤ-
ɰɢɹ ɟɫɬɶ ɜɡɚɢɦɨɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɫɢɝɧɚɥɚ ɢ ɩɨɦɟɯɢ. Ʉɨɪɪɟɥɹɰɢɨɧɧɵɣ
ɢɧɬɟɝɪɚɥ ɩɨ ɢɡɦɟɪɹɟɦɨɦɭ ɩɚɪɚɦɟɬɪɭ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɨɬɧɨɲɟɧɢɹ ɫɢɝɧɚɥ/ɲɭɦ
ɢɦɟɟɬ ɬɚɤɢɟ ɨɫɨɛɟɧɧɨɫɬɢ: ɱɟɦ ɛɨɥɶɲɟ Q, ɬɟɦ ɨɫɬɪɟɟ ɷɬɚ ɮɭɧɤɰɢɹ, ɚ ɡɧɚɱɢɬ, ɬɨɱ-
ɧɟɟ ɦɨɠɟɬ ɛɵɬɶ ɩɪɨɢɡɜɟɞɟɧɚ ɨɰɟɧɤɚ ɩɚɪɚɦɟɬɪɚ a. Ɉɞɧɚɤɨ ɟɫɬɶ ɜɟɪɯɧɢɣ ɩɪɟɞɟɥ
(ɩɨɬɟɧɰɢɚɥɶɧɵɣ) ɩɨɝɪɟɲɧɨɫɬɢ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɚ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɚɦɨɝɨ ɫɢɝɧɚɥɚ
ɛɟɡ ɭɱɟɬɚ ɲɭɦɨɜɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ. ȿɫɥɢ Q>>1, ɬɨ <(a*-a
0
)>=0, ɚ ɟɟ ɞɢɫɩɟɪɫɢɹ
ɪɚɜɧɚ
V
a
2
= [d
2
z
s
(a)/da
2
]
-1
/
0
aa
= -1/[(2E/S
0
) (d
2
k
s
(a)/da
2
)],
ɝɞɟ k
s
(a) =(1/S
0
)
³
T
0
s(t)s(t,a)dt - ɧɨɪɦɢɪɨɜɚɧɧɚɹ ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ ɩɨ ɢɡ-
ɦɟɪɹɟɦɨɦɭ ɩɚɪɚɦɟɬɪɭ. ɉɟɪɟɞ ɜɵɪɚɠɟɧɢɟɦ ɞɥɹ V
a
2
ɫɬɨɢɬ ɦɢɧɭɫ ɢɡ-ɡɚ ɬɨɝɨ, ɱɬɨ
ɫɢɝɧɚɥɶɧɚɹ ɮɭɧɤɰɢɹ ɩɪɢ ɡɧɚɱɟɧɢɢ a = a
0
ɦɚɤɫɢɦɚɥɶɧɚ ɢ ɟɟ ɜɬɨɪɚɹ ɩɪɨɢɡɜɨɞɧɚɹ
ɨɬɪɢɰɚɬɟɥɶɧɚ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɞɢɫɩɟɪɫɢɹ - ɜɟɥɢɱɢɧɚ ɩɨɥɨɠɢɬɟɥɶɧɚɹ.
ȿɫɥɢ a ɟɫɬɶ ɡɚɞɟɪɠɤɚ W, ɬɨ ɨɩɪɟɞɟɥɢɬɶ W* - ɡɧɚɱɢɬ ɧɚɣɬɢ ɩɨɥɨɠɟɧɢɟ ɦɚɤɫɢ-
ɦɭɦɚ ɧɚ ɨɫɢ W, ɢ ɱɟɦ ɨɫɬɪɟɟ k
s
(W)ɩɪɢ W = W
0
, ɬɟɦ ɜɵɲɟ ɬɨɱɧɨɫɬɶ ɨɰɟɧɤɢ W (ɛɨɥɶɲɟ
ɡɧɚɱɟɧɢɟ ɜɬɨɪɨɣ ɩɪɨɢɡɜɨɞɧɨɣ).
Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ k
s
('Z)ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɱɚɫɬɨɬɵ ɩɪɢɯɨɞɹɳɟ-
ɝɨ ɫɢɝɧɚɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɱɚɫɬɨɬɵ ɩɟɪɟɞɚɜɚɟɦɨɝɨ ɫɢɝɧɚɥɚ (ɪɚɞɢɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ
ɨɛɴɟɤɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɭɧɤɬɚ ɧɚɛɥɸɞɟɧɢɹ).
Ɍɨɱɧɨɫɬɢ ɨɰɟɧɨɤ W ɢ 'Z ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɩɨ ɮɨɪɦɭɥɚɦ:
V
W
2
= =1/(2EE
2
/S
0
) ɢ V
:
2
=1/(2ED
2
/S
0
),
ɝɞɟ E
2
=
³
f
f
Z
2
F
2
(Z)d Z/
³
f
f
F
2
(Z)d Z = 'Z
ɷ
2
; 'Z
ɷ
- ɷɮɮɟɤɬɢɜɧɚɹ ɲɢɪɢɧɚ ɫɩɟɤ-
ɬɪɚ ɫɢɝɧɚɥɚ; ɱɢɫɥɢɬɟɥɶ ɜɵɪɚɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɲɢɪɢɧɭ ɫɩɟɤɬɪɚ ɢ ɩɨɞɨɛɟɧ
ɜɵɪɚɠɟɧɢɸ ɞɥɹ ɞɢɫɩɟɪɫɢɢ, ɤɨɬɨɪɚɹ ɩɨɤɚɡɵɜɚɟɬ ɫɬɟɩɟɧɶ ɪɚɡɛɪɨɫɚɧɧɨɫɬɢ ɋȼ, ɚɜ
ɩɪɢɜɟɞɟɧɧɨɣ ɮɨɪɦɭɥɟ - ɫɬɟɩɟɧɶ ɪɚɫɫɟɹɧɢɹ ɫɩɟɤɬɪɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɨɬɧɨɫɢ-
ɬɟɥɶɧɨ Z
0
;
D
2
=
³
f
f
t
2
c
2
(t)dt/
³
f
f
c
2
(t)dt = ('t)
ɷ
2
; 't
ɷ
- ɷɮɮɟɤɬɢɜɧɚɹ ɞɥɢɬɟɥɶɧɨɫɬɶ ɫɢɝɧɚɥɚ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɬɨɛɵ ɩɨɜɵɫɢɬɶ ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɹ ɜɪɟɦɟɧɢ ɡɚɞɟɪɠɤɢ,
ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɲɢɪɢɬɶ ɫɩɟɤɬɪ ɫɢɝɧɚɥɚ, ɚ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɞɥɢɬɟɥɶ-

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