1
() (t) W(w). C m.
:
1. (t) .
2. W(w) (t) .
3. ∆ω τ .
4. () .
5. , (c, d ] - Ρ(c < x ≤ d).
1 2.
1
W(ω) | |
W(ω) = W0∙ω/α, 0 ≤ ω ≤ α; W(ω) = 0, ω > α; | |
W(ω) = W0∙ (1- ω/α), 0 ≤ ω ≤ α; W(ω) = 0, ω > α; | |
W(ω) = W0∙α2 / (α2+ω2); | |
W(ω) = W0∙exp[- ω2/α2]; | |
W(ω) = W0, 0 ≤ ω ≤ α; W(ω) = 0, ω > α; | |
W(ω) = W0, ω0 ≤ ω ≤ ω0+α; ω 0 = 103∙α; W(ω) = 0, ω < ω0, ω > ω0 + α; | |
W(ω) = W0∙ (ω- ω0)/α, ω0 ≤ ω ≤ ω0+α; ω 0 = 103∙α; W(ω) = 0, ω < ω0, ω > ω0+α; | |
W(ω) = W0∙[1 (ω ω0)/α], ω0 ≤ ω ≤ ω0+α; ω0 = 103∙α; W(ω) = 0, ω < ω0, ω > ω0+α; | |
W(ω) = W0∙α2/[α2 + (ω - ω0)2]; ω 0 = 103∙α; | |
W(ω) = W0∙exp[- (ω - ω0)2/α2]; ω 0=103∙α; |
2
W0, 2∙/ | 2∙10-1 | 10-3 | 5∙10-2 | 10-2 | 4∙10-3 | 3∙10 | 6∙10-1 | 2∙10-4 | 0,4 | 2 |
α, / | ||||||||||
m , B | -1 | -2 | -3 | -4 | ||||||
c, B | -1 | -2 | -2,5 | -3 | -4 | -5,5 | -2 | |||
d, B | 2,5 | -0,5 | -1,5 | -2 | 1,5 |
1.
[1- .52-53, 56-59; 2- .46-47; 4- .140-141, 160-164].
[4].
W(ω) (τ) :
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(τ) = 1/(2π)∙∫ W(ω)∙exp(jωτ)∙dω;
W(ω) = ∫ (τ)∙exp(-jωτ)∙dτ; (1.1)
(τ) , W(ω) ω. , , :
(τ) = 1/π ∙ ∫ W(ω) ∙ cos(ωτ)∙dω;
W(ω) = 2 ∙ ∫ (τ) ∙ cos(ωτ)∙dτ; (1.2)
, W(ω) , (1.2) . [4- .161-162] .
(ω0=0) 04 ( 1), (τ) W(ω). 0(τ).
(ω0>>α) 59 [4- .171-172]:
(τ) = 0(τ) ∙ cos(ω0τ), (1.3)
: 0(τ) ( ).
, (τ), - (1.2) ω=ω0+Ω (ω-ω0=Ω) Ω 0 ∞, (. ):
(τ) = 1/π ∙ ∫ W(ω- ω0) ∙ cos(ωτ) ∙ dω = 1/π ∙ ∫ W(Ω) ∙ cos[(ω0+Ω)τ]∙dΩ =
= 1/π ∙ [ ∫ W(Ω) ∙ cos(Ωτ)∙dΩ]∙ cos(ω0τ) - 1/π ∙ [ ∫ W(Ω) ∙ sin(Ωτ)∙dΩ]∙ sin(ω0τ); (1.4)
, ω0 >> α:
(τ) ≈ 1/π ∙ [ ∫ W(Ω) ∙ cos(Ωτ)∙dΩ]∙ cos(ω0τ), (1.5)
0(τ) = 1/π ∙ ∫ W(Ω) ∙ cos(Ωτ)∙dΩ, (1.6)
: W(Ω) , W(ω), ω0.
(1.3) .
:
- 0; 1: (. );
- 2: (. );
- 3: (. );
- 4: ;
- 5: , (1.3) (1.6), W(Ω)= W0;
- 6: (. ), (1.3) (1.6),
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W(Ω)= W0∙ Ω/α;
- 7: (. ), (1.3) (1.6), W(Ω)=W0∙ [1-Ω/α];
- 8: (. ), (1.3) (1.6), W(Ω)=W0∙α2/(α 2+Ω2);
- 9: (. ), (1.3) (1.6), W(Ω)=W0∙exp[-Ω2/α2];
4, 0(τ)=W0∙α/π∙sin(α∙τ)/(α∙τ). 5. . sin(α∙τ)/(α∙τ) τ, : 0(τ)=0 sin(α∙τ)=0; α∙τ=kπ; τ= kπ/α, k=1, 2,..., τ . 0 1 (1-cosX) .
(τ) ω0≠0, 0(τ) τ, ω0 .
∆ω
τ . :
). ∆ω τ . 0(τ) W(ω). W(ω) (τ) [4 .163-164]:
∆ω = ∫W(ω)∙dω / W.(ω), (1.7)
τ = ∫0(τ)∙dτ / 0(0), (1.8)
: W.(ω) ;
0(τ) .
). , . . , ∆ω , W(ω) ≠0. .
). τ 0(τ) τ = 0, τ = τ, 0(τ) ≈ 0,1∙0(0). ∆ω W(ω) ω = 0, ω = ∆ω, W(ω) ≈ 0,1∙W.(ω). ) 0(τ) W(ω).
). τ τ, 0(τ) = 0. , ( 0, 1, 4, 5).
) , (. ), .
() [2- .46; 4- .140]. σ2 (τ):
D(x) = σ2 = (τ=0) = (0). (1.9)
F(x)
Ρ(c < x ≤ d) [ 2- .47, 2.6; 4- .140-141]:
Ρ(c < x ≤ d) = F(d) F(c) = [(d-m)/σ] - [(c-m)/σ], (1.10)
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: m ( ) ;
() .
() = 1/√2π∙∫exp(-t2/2)∙dt; (1.11)
[13] [1] . , . , , .
2
(t)
() (),
3.
:
1. h .
2. - ().
3. ()
- F(x).
4. - F().
5. () D().
3
() | |||||||
c | d | b | e | ||||
0 9 | -2 | -1 | 0,1 | ||||
0,25 | |||||||
1 8 | -1 | 0,2 | |||||
-2 | 0,3 | ||||||
2 7 | 0,25 | ||||||
-3 | 0,28 | ||||||
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6