Подождите немного. Документ загружается.
°
°
L L
L
L L (L + 1)
N > 2
F = (f
0
, . . . , f
N−1
) N F
i
f
i
6= 0 f
i
= f(i∆)
f(t) t ∆
0, . . . , N −1
i = 0
i = 1
L 1 < L < N
K = N − L + 1
X
i
= (f
i−1
, . . . , f
i+L−2
)
T
, 1 ≤ i ≤ K,
L
X
i
L
L
F
X = [X
1
: . . . : X
K
]
X = (x
ij
)
L,K
i,j=1
=
f
0
f
1
f
2
. . . f
K−1
f
1
f
2
f
3
. . . f
K
f
2
f
3
f
4
. . . f
K+1
f
L−1
f
L
f
L+1
. . . f
N−1
.
x
ij
= f
i+j−2
X
i + j = const
L × K
N = L + K − 1
=
S = XX
T
λ
1
, . . . , λ
L
S λ
1
≥ . . . ≥ λ
L
≥ 0
U
1
, . . . , U
L
S
d = max{i : λ
i
> 0} V
i
= X
T
U
i
/
√
λ
i
i = 1, . . . , d X
X = X
1
+ . . . + X
d
,
X
i
=
√
λ
i
U
i
V
T
i
X
i
1
(
√
λ
i
, U
i
, V
i
) i
{1, . . . , d} m
I
1
, . . . , I
m
I = {i
1
, . . . , i
p
} X
I
I
X
I
= X
i
1
+ . . . + X
i
p
.
I = I
1
, . . . , I
m
X = X
I
1
+ . . . + X
I
m
.
I
1
, . . . , I
m
N
Y L × K y
ij
1 ≤ i ≤ L 1 ≤ j ≤ K L
∗
= min(L, K) K
∗
= max(L, K)
N = L + K − 1 y
∗
ij
= y
ij
L < K y
∗
ij
= y
ji
Y g
0
, . . . , g
N−1
g
k
=
1
k + 1
k+1
X
m=1
y
∗
m,k−m+2
0 ≤ k < L
∗
− 1,
1
L
∗
L
∗
X
m=1
y
∗
m,k−m+2
L
∗
−1 ≤ k < K
∗
,
1
N − k
N−K
∗
+1
X
m=k−K
∗
+2
y
∗
m,k−m+2
K
∗
≤ k < N.
i + j = k + 2 k = 0 g
0
= y
11
k = 1
g
1
= (y
12
+y
21
)/2 Y
(h
0
, . . . , h
N−1
)
Y g
i
= h
i
i
X
I
k
e
F
(k)
= (
e
f
(k)
0
, . . . ,
e
f
(k)
N−1
)
(f
0
, . . . , f
N−1
) m
f
n
=
m
X
k=1
e
f
(k)
n
.
F = (f
0
, . . . , f
N−1
)
X
1
, . . . , X
K
X
i
= (f
i−1
, . . . , f
i+L−2
)
T
∈ IR
L
K = N − L + 1
L 2 ≤ L ≤ N − 1
X
i
X
j
L K
K → ∞
L
X
i
L
X
i
L
L
F = (f
0
, . . . , f
N−1
)
X
X
T
(f
0
, . . . , f
N−1
)
K = N − L + 1 L