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ao coo a cpyypa cxea, e cea pcycy oo p a coee: apaeoe, oceoaeoe c opao c. aae paccope o coee ec oyee coooe ey epeaoo ye coee epeao y oex ee.

5.3.2 apaeoe coeee ee p apaeo coee (pc. 5.28) ca xoa cex ee oao pa cay xoa cce x(t), a xo y(t) pae cye cao xoo ee.

yx Wy2 y x x Wyx WPc. 5.28 apaeoe coeee ee aoo ea oepaopo ope oo aca:

y1(s) = x(s)W1(s); y2 (s) = x(s)W2(s);...; yn (s) = x(s)Wn (s), oa xo ce cce n y(s) = y1(s) +... + yn(s) = x(s)[W1(s) +... +Wn(s)] = x(s) (s), (5.78) W i i=oya epeaoa y apaeoo coee n y(s) Wc (s) = = (s). (5.79) Wi x(s) i =Ta opao, nepeamoa yu cucme napaeo coeuex ee paa cye nepeamox yu omex ee.

Bpeee xapaepc, acoc, epexoy y oo oy (5.79):

n n hc (t) = L-1[h(s)] = L-1 (s) = (t), (5.80) hi hi i = i=.e. epexoa y apaeoo coee paa cye epexox y oex ee.

acoe xapaepc apaeoo coee oya cey opao:

n n Wc (i) = (i) = Re () + i Im () ;

W j j j j =1 j =n n Rec () = (); Imc () = (). (5.81) Rei Imi i=1 i =a o (5.81), ayo-aoa xapaepca apaeoo coee oe oyea peyae coe ecex x ace AX oex ee o pay coe eopo. Ha pc. 5.29 peea cpa oye AX yx apaeo coeex ee, aax co AX.

a) ) ) Im Im Im k1 k2 k1 + kW1(i 1) 0 0 Re W2(i 1) Re Re W2(i 1) W1(i 1) W(i 1) Pc. 5.29 ocpoee AX apaeoo coee:

a AX epoo ea; AX opoo ea;

AX apaeoo coee epoo opoo ee pepo exooecoo oea, eeo ooy cpyypy cxey, oe cy eoa apaeo paoax oox peaopo (pc. 5.30).

Cpe poy Cop Pc. 5.30 pep exooecoo oea apaeoo coee 5.2.3 oceoaeoe coeee ee p oceoaeo coee xo peyeo ea oaec a xo oceyeo (pc. 5.31).

pae xox cao oce aoo ea oepaopo ope e :

y1(s) = x(s)W1(s); y2 (s) = y1(s)W2 (s);...; yn (s) = yn-1(s)Wn (s).

y1 y2 yn xW1 W2 Wn Pc. 5.31 oceoaeoe coeee ee Bxoo ca oceeo ea ec xoo ce cce: y(s) = yn(s), a epeaoa y cce coaco opeee ee y(s) yn (s) Wc (s) = =.

x(s) x(s) poo oceoaey ocaoy, oya epeaoy y oceoaeoo coee n Wc (s) = W1(s)W2(s)... Wn (s) = (s). (5.82) Wi i=Ta opao, nepeamoa yu cucme noceoameo coeuex ee paa npoueeu nepeamox yu omex ee.

acoe xapaepc eo oya (5.82), a a n i () j n n j Wc (i) = (i) = ()e, W j M j j =1 j =oa n n Mc () = (); c () = (), (5.83) Mi i j =1 j =.e. ayo-acoa xapaepca oceoaeoo coee paa poee AX oex ee, a ao-acoa cye X oex ee.

cpa ocpoe AX yx oceoaeo coeex ee, aax co AX, peea a pc. 5.32.

epexoy y oya cey opao. Ec xoo ca x(t) = 1(t), o a xoe epoo ea ee eo epexoy y h1(t), oopa oaec a xo opoo ea. Ha xoe opoo ea oya epexoy y yx oceoaeo coa) ) ) Im Im Im k1 k2 k1 k1+2 Re Re Re MMM1 MPc. 5.32 ocpoee AX oceoaeoo coee:

a AX epoo ea; AX opoo ea;

AX oceoaeoo coee epoo opoo ee eex ee. Ec cocea epexoa y opoo ea h2(t), o epexoa y coee opeec epe epa ae:

t dh1(t - ) hc (t) = () (5.84) h d d + h1(0)h2(t).

pooa paccye ae, oo oy paee epexoo y oo ca oceoaeo coeex ee.

Ceye oe, o ce oyee yepe cpae oo ee apaeoo ec.

pepo exooecoo oea, eeo cpyypy cxey oceoaeoo coee, ec o exooec poecc, oopo oee ca yac pecac e cooecyeo ea.

5.3.4 Coeee c opao c Opao c aa epeay caa c xoa ea a eo xo, e ca opao c aepaec cypyec c e cao. Cpyypa cxea coee c opao c opaea a pc. 5.33.

Ec x1 = x + xoc, o c aaec ooeo, ec e x1 = x - xoc, o opaeo.

oa epeaoo y coee c ooeo opao c xoe ca aoo ea oepaopo ope acac a:

y(s) = x1(s)W p (s); x1(s) = x(s) + xoc(s); xoc(s) = y(s)Woc(s).

ca oyeo cce x1(s) xoc(s), oya y(s) = x(s)W p (s) + y(s)Woc (s)W p (s) ;

y(s)(1-Woc (s)W p(s)) = x(s)W p (s), oya nepeamoa yu coeueu c nooumeo opamo c ee y x1 Wp(s) x xoc Woc(s) Pc. 5.33 Coeee c opao c W p(s) y(s) Wc (s) = =. (5.85) x(s) 1-W p (s)Woc (s) coeueu c ompuameo opamo c epeaoa y oc aao opao opeeec ooaeo e paee W p (s) Wc (s) =. (5.85) 1+ W p (s)Woc(s) Ha pae aoee pacpocpae c cce c opaeo opao c, oocc, apep, ce oooype cce aoaecoo peypoa, pe po e pacooe oe, a opao peyop.

5.3.5 epeaoe y ayo cce Cpyypa cxea oooypo cce aoaecoo peypoa peea a pc. 5.34.

f0(t) ya y(t) Wp(s) Wo(s) y Pc. 5.34 Cpyypa cxea oooypo cce B paceax cce aoaecoo peypoa coy p ocox a epeaox y. y opeec cey opao.

ao epeaoo ye ec nepeamoa yu no aay peyupoau ya - y(t), f0(0) = 0 :

Wo (s)Wp (s) W (s) =. (5.86) 1+Wo (s)Wp (s) epeamoa yu aymo cucme ouu, .e. o aay ya - (t), e (t) = ya(t) - y(t) oa peypoa f0(t) = 0:

W(s) =. (5.87) 1+ Wo (s)Wp (s) epeamoa yu aymo cucme no oyaey oecmu, .e. o aay f0(t) - y(t)= 0 :

Wo (s) W (s) =. (5.88) f 1+Wo (s)Wp (s) Aa epeaox y ayo cce oaae, o aeae y x o o e, a ce pa. ayo cce oo aca e p pyx epeaox y, apep, o o oyaey oec.

Xapaepcecoe ypaee ayo cce axoc aeaee epeaoo y acaec e 1+Wo (s)Wp (s) = 0. (5.89) op oo ypae pa oca si epeaoo y ayo cce.

aece coca poecco, poeax ayo ccee, cyeceo oac o aox paoyo e, cocoe ex e cax ee. Ta a epeaoa y paoyo e acaec e Wp.c(s) = Wo(s)Wp(s), o aa epeaoa y oe acaa a Wp.c (s) W (s) =.

1+Wp.c (s) 5.3.6 paa peopaoa cpyypx cxe Peae oe oaa coo cpyypo. poee oa epeaox y cox oeo cxeax ocaec a ce peopaoa x cpyypx cxe pe oco a coee.

pep paoc peopaoa cpyypo cxe aaec o, o xoe xoe ca peopayeoo yaca o oce peopaoa oao.

Ha pae peo cpeac cxe, oopx oo cpay e e o o coee, a pao, ec, a aaee, epepece c. B o cyae oae eoxooc epecao epeoca cyaopo yo.

Hapep, peyec ocyec epeoc ya epe eo o apae pacpocpae caa (pc. 5.35, a).

peopaoa oe yaco, ee ypo, oop ee o xoo ca x(t) a xox x(t) y (t). Tpeyec epeec ye "1" epe eo "2" c epeaoo ye W(s).

poco epeoc po cxee, opaeo a (pc. 5.35, ). a cxea e cooecye cxoo, a a ocycye xoo ca x(t), o eec a caa y(t), pe y(s) = x(s) W(s), ceoaeo, pee cxe cxoo eoxoo ooy e a xoe y(t) eo c epeaoo ye. Toa W (s) oya cxey (pc. 5.35, ), cooecyy cxoo.

a) ) (2) (2) y (1) y (1) x x W(s) W(s) y x ) (2) y (1) x W(s) 1/W(s) y Pc. 5.35 pep epeoca ya epe eo:

a o peopaoa; epaoe peopaoae; oce peopaoa Ta opao, epeoc ya epe eo c epeaoo ye W(s) o apae pacpocpae caa copooaec oee ooo e ea, eeo epeaoy y.

W (s) Paccope pep ec oaaeco paa epeoca ya epe eo.

Ocae paa epeoca poc e oaaeca cey opao.

1 epeoc ya epe ye ocyecec e ooex peopaoa (pc.

5.36).

a) ) x (1) (2) x x x (2) (1) x x x x Pc. 5.36 epeoc ya epe ye:

a o epeoca; oce epeoca 2 epeoc cyaopa epe cyaop pooc e ooex peopaoa (o epee ec caaex cya e eec) (pc. 5.37).

x1 + x2 x1 + x2 + x3 x1 + x3 x1 + x2 + xx1 xx2 x3 xxPc. 5.37 epeoc cyaopa epe cyaop:

a o peopaoa; oce peopaoa 3 p epeoce ya epe cyaop o apae caa ooo e peopaoaoo yaca oec ooeoe eo c epeaoo ye (-1) (pc. 5.38).

) a) x1 x1 + x2 x1 x1 + xxxxxPc. 5.38 epeoc ya epe cyaop:

a o peopaoa; oce peopaoa 4 p epeoce cyaopa epe ye o apae caa ooo e oec eo c epeaoo ye +1 (pc. 5.39).

) x1 + xx1 + x2 a) xxx1 + xxxx1 + xPc. 5.39 epeoc cyaopa epe eo:

a o peopaoa; oce peopaoa 5 epeoc ya epe eo o apae caa po oe ooeoo ea c epeaoo ye (pc. 5.40).

W (s) a) ) x x W(s) x W(s) x W(s) W(s) x 1/W(s) x Pc. 5.40 epeoc ya epe eo:

a o peopaoa; oce peopaoa 6 p epeoce ya epe eo po apae caa oec ooeoe eo c epeaoo ye W(s) (pc. 5.41).

a) ) x W(s) x W(s) x x W(s) W(s) x W(s) W(s) x W(s) Pc. 5.41 epeoc ea epe ye:

a o peopaoa; oce peopaoa 7 epeoc cyaopa epe eo o apae caa copooaec oee ooeoo ea c epeaoo ye W(s) (pc. 5.42).

a) ) x1 + x2 W(s) W(x1 + x2) x1 x1 W(s) W(x1 + x2) xW(s) xPc. 5.42 epeoc cyaopa epe eo:

a o peopaoa; oce peopaoa 8 epeoc cyaopa epe eo po apae caa po oe ooeoo ea c epeaoo ye (pc. 5.43).

W (s) ) a) x1 W(s) x1W + xx1 W(s) x1 W + x1/W(s) xxPc. 5.43 epeoc ea epe cyaop:

a o peopaoa; oce peopaoa 9 Becee eea po c po oe ooex ee, po e ooeo W2(s) (pc. 5.44).

W (s) a) ) W1(s) W1(s) 1/W2(s) y y x x W2(s) W2(s) Pc. 5.44 Becee eea po c:

a o peopaoa; oce peopaoa 10 Becee eea py c copooaec oee oo opo px ex ee c epeaoo ye W2(s) ooeo e ea c epeaoo ye (pc. 5.45).

W (s) a) ) W1(s) W1(s) W2(s) y y x x 1/W2(s) W2(s) Pc. 5.45 Becee eea py c:

a o peopaoa; oce peopaoa 11 Becee eea opao c copooaec oee po e eea c epeaoo ye W2(s), a ooeo e ea c epeaoo ye (pc. 5.46).

W (s) a) ) x y W1(s) x y 1/W2(s) W2(s) W1(s) W2(s) Pc. 5.46 Becee eea opao c:

a o peopaoa; oce peopaoa 12 Becee eea opay c copooaec oee opao c ea c epeaoo ye W2(s), po e ea c epeaoo ye, ooeo ea c epeaoo ye W2(s) (pc. 5.47).

W2 (s) a) ) x y x y W1(s) W2(s) 1/W2(s) W1(s) W2(s) Pc. 5.47 Becee eea opay c:

a o peopaoa; oce peopaoa puep 5.1 aca epeaoy y coee, opaeoo a pc. 5.48.

W2(s) y x W1(s) W3(s) W5(s) W4(s) W6(s) Pc. 5.48 Cpyypa cxea eoopoo oea W5(s) W (s) = W1(s)[W2(s) + W3(s) + W4 (s)].

1-W5(s)W6(s) puep 5.2 peopaoa cpyypy cxey (pc. 5.49) aca epeaoy y a) 1 1 2 W1(s) W3(s) W2(s) ) 2 1 W1(s) W3(s) W2(s) 1/W3(s) Pc. 5.49 Cpyypa cxea eoopoo oea c epepec c:

a o peopaoa; oce peopaoa W1 s W2 s W3 s W s =.

1+W1 s W2 s + W2 s W3 s + W1 s W2 s W3 s 5.3.7 opya Mecoa p oe epeaox y cox cpyypx cxe e cea ae yoo ooac paa peopaoa. B 1953 . Mcoo o peoeo pao ce epeaoo y ey y aa ya. o pao paaec ceye opyo b r np (s) pi (s)) W (1+W j j =1 i=Wmn (s) =, (5.90) b pi (1+W (s)) i= r e Wmn(s) epeaoa y ey ya m n; (s) cya r epeaox Wnp j j =y pax px ye ya m ye n; Wpi (s) - epeaoa y paoyoo oypa, a co ao, cooecy opaeo opao c;

- poeee, aee ce aye oyp cce; * - a ooaae cee co cex eo, coepax poee epeaox y ox ex e ee, a e c W(s) = 1.

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