004


.., ... ,
, . ,

. , , , , , . , , ().
:
1. , [1]. - .
2. , [2]. - .
3. [3]. - .
4. , [4]. - .
5. [1]. - .
, .
, ,
42
"" . .-2012.-49

[5]. , , .
, .
:
- ;
- ;
- ;
- ;
- , ;
- , , ;
- .

, , , . , . [6].
( , ) .
SN = {s}, SN [0,...S - 1}N -
s N , rS - ()
. SN .
' If If
V = {v}, V [a, b] - v K , a, b - , a < b. rV ().
V K .
K < N,
V

<
S
N
"" . .-2012.-49
43

' ' '
X = {x}, X {0,...,2X -1} -
x K, rX - () -

. X .
rX < rS, rX < rV, K < N,
X
K
<
V
K
X
K
<
S
N
YM = {y}, YM {0,1}M - M. YM .
Y
M
<
X
K
Y
M
<
V
K
Y
M
<
S
N


, , .
SN
N
d (si, s j) =2
s. s
*jn
n=1
U J e1,
S
N
, i * j
V K
K
d (vi, v j) = 2
k=1
vik - v Jk
, i, j 1,
V
K
i * j .
X K
K
d(xi, xj) = 2 |xikxjk [i, 1,
k=1
X
K
i * J.
YM
M
d (y , y j) = 2
k=1
- y
i, j 1,
Y
M
i * j.

, , .
44
"" . .-2012.-49

SN VK : S ^ V , - , , -. .
K K
V X
' '
: V ^ X , - , ,
-. .
XK YM : XK ^ YM , . .

, , . , . .
ES = {(s, s) | s, s SN () = ()} SN SN - SN. ES DS = {SN}, SN
|vk| _
SN = SN , V/, j ,
=
SiN
SN = {z | z, s SN vi = () (z, s) ES } SN, vi VK, .
EV = {(v, v) | v, v VK (v) = ()} VK VK - V .
'
EV DV = {V/ }, VK
V

* j SN n SN = 0.
N
"" . .-2012.-49
45

X

VK = Vf, Vi, j , XK,i * J viK nv
i=1
K
0.

V




ViK = {z | z, v VK A xi = (v) A (z, v) Ev } c VK, xi XK,
.
EX = {(X, x) | X, x XK a () = ()} c XK x XK -

rK

X .
'
EX DX = {Xi },
XK
Y
M
XK = XK , Vi, J , YM , J XK n Xj =0,
=1
X


Xi
= {z | z, x X A yi =(x) A (z, x) EX } c X,

yi YM,
.
,
, .
SN (SN, ) p(s, s)
,
Vs, s SN p(s, s)
1, d (s, s) > 0
0, d (s, s) = 0.
SN (SN, ) , .. dim SN = 0. SN (SN, ) .
SN, (SiN, ). SN (SN, ) .
V -
'
(V , ) (V, v) ,
46
"" . .-2012.-49

Vv, v (v, v)
1, d (v, v) > 0
0, d (v, v) = 0
1C
V (V , ) -
1C
, .. dim V = 0. V
'
(V , ) . VK -
1C 1C
(V , ). V (ViK , ) .
-
'
(X , ) (, ) ,
VX, (, )
1, d (, ) > 0
0, d (, ) = 0.
' '
X (X , ) -
1C 1C
, .. dim X = 0. X
'
(X , ) .
X i ( Xi , ) . Xi -
'
(X , ) .
YM (YM, ) (, ) ,
Vy, yM (, )
1, d (, ) > 0
0, d (, ) = 0.
YM (YM, ) , .. dim YM = 0. YM (YM, ) . , , , , , .
(SN, )
"" . .-2012.-49
47

'
: S ^ V . (SN, p) -
N
: S ^ V , ..
Vs,s SN Vs> 0 38 > 0 : p(s,s) <8^-((s),(s)) <s.
'
, : S ^ V , (SN, ) '
(V , ),
V^ S sN ^ s) > ( (sX (s)), () .
'
(V , )
' '
: V ^ X .
'
(V , ) -
1C 1C
^ : V ^ X , ..
Vv,vV Vs>0 38>0 : (,v)<8^-((v),Vp(v))<s.
1C 1C
, : V ^ X , '
(V , )
'
(X , ),
Vv, v evK (, v) >(^ (vX Vp (v)), () .
'
(X , ) : XK ^ YM .
'
(X , ) : XK ^ YM , ..
Vx,XK Vs>0 38>0 : (,x)<8^((),())<s.
, : XK ^ YM, -
'
(X , ) (YM, ),
Vx, XK (, ) > ((), ()), () .
, ( , ),
48
"" . .-2012.-49

. , , , . 1. . s = (sb...,sN) ; v = (vb...,vK) ; x = (x1,...,xK) ; y = (y1,...,yM).
: SN ^ VK , - = (s). . 1. -
' '
: V ^ X , i - xi xi = (v). : XK ^ YM
, i - x -
'
(X , ) yt = (x).
y = F(s, , ),
= ( ( (s),... , (s)),... (1 (s),... , (s))),i ^ 1 M.
:
1. ,
'
, : SN ^ VK
' '
: V ^ X , J = T ^ min.
,
2. ,
'
, : SN ^ VK
' '
: V ^ X ,
1
J = ^Zp(f(sp,,),p) ^ min,
p=i ,
"" 49
. .-2012.-49

(F (s p, ,), p)
1, d (F (s p, a, p),y p) > 0
0, d (F (s p, a, p),y p) = 0
s p - , y p - , P -
.
3. , a, :SN ^VK :VK ^XK, 1 p
J = - (F(sp,a,p) - yp) (F(sp,) - yp) ^ min.
P p=1
,

1. , , , .
2. , . () .
3. .
4. , , .
5. .

1. . / . . - .: , 2002. - 344 .
2. . : / . . - .: ї, 2006. - 1104 .
3. .. / .. , .. . - .: - . .. , 2002. - 320
4. . / . . - .: ї, 2001. - 288 .
5. . / . . - .: , 2005. - 671 .
6. .. / .. . - : - ї, 2010. - 303 .
50
"" . .-2012.-49

.. . , , . ' .
: , , , , , '.
.. . , , . .
: , , , , , .
Fedorov .. Method of signal processing on the basis of non-expansive uniformly continuous mapping. In article the method of signal processing on the basis of non-expansive uniformly continuous mapping operating in compact metric spaces which provides construction of effective model of signal patterns classification is developed. The offered method is intended for technical and biological objects identification and control of their condition.
Keywords: signal processing, classification model, non-expansive uniformly continuous mapping, compact metric spaces, discrete sets, identification and control condition objects.
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