o
npfipoAHoM
lrpouecce,
o.{,HaKo
3TH
npeAcTaBJIeHHfl,
KoHeqHO,
He
TaK no,/'lHo
oTpax(aIoT
AeftcTBHTe,rIbHocTb,
KaK
N,toAe"rllI
c
pacnpereireHHbrMH
napaMerpaMH.
OAHaro il,roAeJrH
c
cocpe-
AoroqeHHbIMII
[apaNrerpaMn rpe6yrcr
MeHbrrre
HcxoAuoft
HH-
Qoprur
arrvrr lr
pacr{erbr
no Hr4M 3HarrHTe,TbHo
6olee npocrbre.
I-loerovry
MoAerI'I
c cocpeAororleHHbIMH
napaMerpaN{H
H no-
fiyrlpi,'r[ [rHpoKoe npaKTHriecKoe pacnpocTpaHeHHe.
3aAaqpr
u4enru{HKaTIHH
npHMeHHTeJrbHo
K
MoAeflcM
pac-
qera
HeycraHoBnB[rerocfl
ABH)KeHHn
BoAbr.
MoAeln
pacrieTa
ocyiqecrB/Tfler npeo6pa3oBaHHe
BxoAFrbrx
traHHbix
X(t)
(na-
npnMep,
pacxoAoB
BoAbr
qepe3
I3U)
B rapaMerpbr
ynpaBJre=
HHfi.
Y
(t)
c noMorr{bro
HeKoroporo
3aKoHa
(oneparopa)
npe-
o6pason
aHvrfl,
^F, r.
e.
Y
(t7
-
F
[x
(t)1.
(6
2)
B xaqecrBe
oneparopoB npeo6pa3oB
aHafl.
Moryr Bbrcrynarb
e
o6qev cfiyrrae oreparopbr
anQQepeHrrupoBaHHfl,,
Htrerpnpo-
BaHHfl,
wnw 6onee
rpocrtre
QynruIHH
npeo6pa3oBaHufl.
Onepa-
Topbr
npeo6pa3oBaHHff
Moryr
6trrt KaK JrLrleftuurvru,
TaK H He-
nnHerirHsrtra,
3aBHCfiu{HMW-
ltilw He 3aBHcflu{HN{H
or
Bperv{eHH
(e
nocre,4HeM
cryqae-crar{HoHapHnre)
.
fIpnueHlITeJIbHo
K
paccMarpHBaeMbINI
AIdHaN{HrlecKI{,.vr
cH-
cTeMaM
ycJroBHfl
CTaUHOHapHOCTH
B HeKOTOpbre
nepHoAbr Bpe-
MeHH
o6rtquo noJiararor
BbrrroJrHeHHbrMH
(e
ern nepnoAbr
yc"To-
BHfr,
Sopur't
poBaHHff
croKa
Mo>KHo rro,r'i?r?Tb
HeH3MeHHnruu).
Ann
nHserlHnrx
crarruoHapHbrx
cncrer{
oneparopoM
npeo6-
pasoBaHHfl
6yaer
o6rrxHoeeHHoe
anQQepeHrruaJrbHoe
ypaBHe-
Hrie
c nocroflHHblMu
rcoeQQnuueuTar,{u, pe[reHne
Koroporo rrpn
Hy,/reBbrx
r{aqaJrbHbrx
yc",'roBnffx
cBoAHTcfi
K
HHTerpaJry
Aroa-
Me/'rfl, floJryqlrBrxevry
pac[pocTpaHeHHe
B npaKTHKe
fHApo/rorH-
qecKHX
pacr{eroB
[39]:
t
Y
(t\
-
.\
p
rt
--
")
x
(=)
dr,
0
rAe P
(t-r)
-nepexoAHafl
Qynxur.rn
Hirvr
QyHxuHn
(a
rHApoJrorHH
oHa
Ha3brBaercfl
xpasofi
a,o6eraHan).
3ra
Qynxuias
c6naAaer
pfir,oNr
ceor?cre
P
(t
-
r,)
oreparopoB npeo6pa3o-
(t)
d;,
fAeP(t,t)flBJIfieTcfiQytixuilefiHeToJlbKooT('-t),HolI
,
(/,
")
B
nocJIeAHeM
cJIYqae
He
ra3ue
3rHX
QYnruufi
nPHMeHH-
IM.
e
uuonoo6pasue
3aKoHoB
Yrl-
PatsJleHKx,
r\\rr
Aa
Jrrt
uq^vr'--
\flleparopsi)
gelUrret?Hli'
|IpuueuHTeJlbrioKMOAeJI'IMpacueraHeycTaHoBHBI.IIerocfl
ABHIKeHHI
so.,I,bl
ueo6xoAlalvto
perirlll
-1"-:,salaqu
u4eutHSu-
Karrun-u4eHrr'rQuKaunro
crpymypu
MoAe/IH
(noncx
3aKoHa'
T.
e.
onepaTopa
-YirpaB.jIeHI{s-F}
v-
tAenru&HKaqHIO
napaMer-
poB
tvloAe.,[H trJrfl
3aAaHHOfO
HJII'I
Ka]hAoro
BapbHpyeMoro
3a-
KOHA.
Eo.nee
rpy:,Hofi
gaAaqeii
ffBJIflercfl
llAentn$HKaqnfl
crpyK-
:
ABa
pa3rIIqHbIX
noAxo4a'
fipn
alKeHHfflv{
3aAaercf
PnA
crPYK-
HX
CONOCTABJICHHff
HAXOAHTCfl
:TCfl
OIITI4Ma,'IbHaf
CTPYKTYPa
TKoPHO
YCTaHOB/ieHHO|O
KJIaCCa
oneparopoB
repexoAa.
r.
c. Ky;ir;;;legl
,
ncnonb3yn
reopHlo
HeKoppeKrHbrx
3a/laq,
pa3pa6otarr
qHcJIeHHltIi tueroA
Haxox{AeHHfl
onrnMaJIb-
Hori
QynxrHH;;;";;
P
V)
B
(6'2)
'
r'
e'
onr,Marsuoi'
crpyK-
Typbt;tuHeftuofiMOAeJIHccocpeAoToIIeHHbIMHnapaMeTpaMH
!,,'Ifl
CTaUHOHaPHOTO
nPOUecCa'
OAHar<o
nir6otouiliii
rpaKr'r{ecxHfi
liHTepec
npeAcTaB"Ifi-
I.OT
H eJiH
n
eir
H
tt e
3
a KO
H
bl
yn-p a
B,,'I
eHHfl
-H
en
u
u
etiulte
O11
ep
aT6
p
bI
F
(uenuHeri*oi.
n"o.""li
at"
M.AeJII'I
Jlyque
orBer{arct
SuaH-
qecKHM
npeACTaBJeHHffM
o
ABH}KeHHH
BoAHofo
noToKa,
a
TaK.
x(e
pes.rbHoivl|
BH-A,y
HCXOAHbIX
XapaKTepHcTHK
pycJla
peKH'
BoAHoro
noroiu-;-;.
n.
oourHa
a:Harr:r^s
ue"uuHeitHltx
cHcreM
Mo}KeTnpoH3BoAHTbcflcnoMolqbloH3BecTHo|oBMaTeMaTHKe
pfl,^aBo,lilreppa,ecJHBbIXoAHaflBe,-'IIiI{HHagelngefiHotlCH.
creMbr
c,,'r3oo
3aBHclir
or
orAa,TeHHoro
npotujiofo
Ha
ee
BXoAe:
+30
..
(.
/ \.-/t -\;
tJ
(,t)
--
\
P,
(",) x
(/
-
"')
d"
t'
-r
Pr("r,
"r)
x(/
-
"r)
x(t
-
'"r)
d'rd'',+
"'
i2,...,
rn)
x
\t
-
",)
x
(f
-
".)
...x
(t
-
"n)
drrdrr
"'
d*n'
., ti)
-QYHt<ur4H
BItufl
HlIr'
(6.31
BJIH'IHHff
-
0 nplr
@
r
/(',
I
P(t)dt-L
K
Ap.
0
Ann
HecraquoHapHbrx esseftHstx
BaHHfl
peirreHHernr
6ya,er
ypaBHeHHe
t
a
Y(.t)-\P(t,-,)X
!
0
\ptr
I
I
n
\
-1'
_:E
+n
+T
.'i'
-+-
\ \
,-,"1
-&
-T
+rc
.t
,.
-+
\
'..
rJ
r86
rAe
P,
(t', tr,
tR7