, :
y (t)= y (ti)[ 1 (t-jT)- 1 (t- (j+ 1) T)]= y (ti) Hj, (3.32)
j = 0, 1, 2,...; tj = jT.
Hj
Hj = 1 (t-jT)- 1 [ t- (j+ 1) T)], (3.33)
, . , . .
. 3.10.
0, . . , 1, . . . 3.10. j , () . i Δ t, i. i = 0. i Δ t : ) , ; ) .
ui uki (k = 1, 2, 3,...) (i Δ t), Hi (3.44), (3.43). .
. . 3.11. . 3.12. Ux,
(3.34)
i = 0 L , :
U ,,= d (t-i D t), i =... -2, -1, 0, 1, 2, 3, , (3.35)
= U , t < N0, (3.36)
N D t<t< (N+ 1)D t. (3.37)
t 1 N 0, Ux U0. ,
(3.38)
(3.39)
. 3.12.
j=l
(3.40)
t2 .
U =d(Uy)=d(t-t2) (3.41)
(), .
t2. , , U :
(3.42)
(3.39) :
. (3.43)
Ux .
t2
(3.44)
N (3.37) ,
|
|
(N0+N)D t<t2< (N0+N+1)D t. (3.45)
t2 D ti,
(3.46)
0<D2£D tN+1 , (3.47)
0<D2 f2N£ 1. (3.47)
(3.43) (3.46)
(3.48)
, x=Ux., y=N. Δ z = Δ 2 f 2CP , .
, U. , . . (3.48) k1=k2, f1.=f2., U=0, . . :
(N/N0) U0<U*x .< [(N+ 1)/ N0 ] U0. (3.49)
(3.48)
(3.50)
T=2N 0 Dt+MDt, Μ , .
(3.34), (3.36), (3.37), (3.39) t, .
3.3. .
. :
1) , ,
2) ,
3) ( , , ).
. .
1. , , . . . . 3.13 , ( ) .
. 3.13. N
2. Δφ,
Δφ= (3.51)
G , r, I ( ), k ( ), .
3. :
(3.52)
E Df; R .
4. () , ( ), ,
(3.53)
|
|
i0 t; e .
5. , , () , , , . .
(3.54)
, R , i , f .
:
1) , ,
2) , ,
3) .
, , .
. , . . x1, , xm-1 . . .
:
1) ,
2) ( , ),
3) , .
() z.
. , , .
1. , ,
, (3.55)
, R , , D V , , = const.
2.
(3.56)
, Μ , R , .
:
3. , .
4. , , , , .
, , .
. b1, ,bi 1, ,ak [11]:
(3.57)
, aj aj0 , :
(3.58)
, , :
1) ,
2) , .
. , , .
:
1. x1,, xm, , , .
2. ; , . . , .
|
|
3. , . .
.
. ( ). () Sx (ω). , X . y=f(x) Y.
1- . . a1, , ak, p (a1, , ak) p1 (a1, , ak). b1, , bi, (3.57) i=1, 2,..., l, :
ψ i : , aj . . 3.1.
2- . . : Sx (ω) Κx(τ) , [12].
(3.59)
(3.60)
( ) . .
3.1.
Z = f (X), X =w(X) | ||
Z = X+Y | ||
Z = X-Y | ||
Z = XY | ||
Z = X / Y |
X , (E [ X ] = 0), .
Y = X 2, (3.61)
,
X1=X (t), X2=X (t+ t), (3.62)
Ky (t)= E {[ X12-E (X12)][ X22-E (X22)]}. (3.63)
Ky (t)=2[ Kx (t)]2.(3.64)
. (3.65)
(3.65)
, (3.66)
.
:
Y=b0+b1X+b2X 2, (3.67)
X , ,
, (3.68)
. (3.69)
Y=XU, (3.70)
E(X)=E(U)=0, X, U , ,
, (3.71)
. (3.72)
(3.67), (3.70) . , .