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) aae cce, oopx aoaec ec ae ya, cocee apaep cpyypa p epeex eex ex yco a ocoa aaa coco oee cce a, o coxpaoc aaoe aeco ee pao. Cce c eee aaoo ae peypyeo e aa cpea, c eee apaepo caoacpaac, c eee cpyyp caoopayc.

1.6 TPEHPOBOHE AAH 1 Ha pc. 1.12 opae oe c xo xo caa.

A o aoe oe ypae pee ope pep.

B ae ee epeee c ypa C aa epeea ec ypaeo epeeo u1(t) un(t)...

x1(t) y1(t) Oe xl(t) ym(t) Pc. 1.12 Oe 2 Ha pc. 1.13 opaea cpyypa cxea cce aoaecoo peypoa.

x Peyop xp y x Oe ya Peyop Pc. 1.13 Cpyypa cxea ACP A ae p peypoa peaoa CAP, opaeo a pc. 1.13 B o a peypoae o ooe C aa ccea peypoa ec aoee eo 3 Ha ae ocoe acc ec cce aoaecoo peypoa A aoy accy oocc ea ccea B Ha ae oacc ec acc "xapaep yopoa" C o pecae coo acc "xapaep oa cao" 1.7 TECT 1 ao poecc aaec exaae A Cooyoc oepa ypae.

B aea pya eoea paox oepax paoo a exao.

C aea pya eoea oepax ypae.

2 Ccey ypae opay:

A Cooyoc cpec ypae oea.

B Cooyoc cpec ypae.

C Oe ypae.

3 e xapaepyec o ee cce A Bxoo oopao.

...

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B Bxoo oopao.

C Bxoo xoo oopaa.

4 ao p peypoa peaoa epo poeo peyope ypo oe apoo a, opeeo . oyo.

A Peypoae "o ooe".

B Peypoae "o oye".

C opoaoe peypoae.

5 aa ccea peypoa aaec aoaeco A Bce paoe oepa oepa ypae o aoaece ycpoca.

B ac oepa ypae o aoaece ycpoca, pyy ac oe eoe.

C Paoe oepa o a exa, a oepa ypae eoe.

6 eeppoae cce ypae opaa:

A Xapaep oa cao.

B Xapaep poecca ypae.

C Xapaep yopoa.

7 p acca cce ypae o xapaepy yopoa ccea aoaecoo peypoa oe :

A Cceo popaoo peypoa.

B Cceo c pacpeee apaepa.

C Coxaceco cceo.

8 Ccea aoaeco caa o ccea, oopo oepaec:

A ya(t) = const.

B ya(t) = f(t).

C ya = f(x).

9 o oco a ypae a poecco ypae cce opaec a:

A Hepepe cpee.

B eeppoae coxacece.

C ee eee.

10 B oax cceax ypae oaae eoc ac o:

A Teyx ae oopa.

B Teyx ae oopa, a ae xapaepa x ee poo, acoe yye.

C Cocex apaepo cce cpyyp.

2 PEPHE CHA X XAPATEPCT B eop aoaecoo ypae p paccope ex x cce e eco pae oec ca. Aa ce opex aoaecx cce cyeceo ypoaec, ec ooac papaoao ae x oec cao. Maeaec pecaee cao ec eoopa y pee, opeea ao eo ee, aoe e eaco o eco ppo. B acoc o xapaepa ee caa o pee, op aeaecoo pecae paa peype eeppoae epeype cyae ca.

2.1 OPEEEHE PEPHOO CHAA Ca aaec peyp, ec eo aeaec pecaee ec apaee aaa y pee, .e. o ocaec opeo ye pee.

Pea e ca paccapaec a cya poecc, opeee epooc xapaepca, a a e apaee pee eo eee o pee.

Bpaee peypoo caa, opeeeoo ye pee, aa pee npecmaeue cuaa. opa ac x y paa. Oo op ac ec pecaee e pooepecoo pa, a e oopoo ec pocee apoeco ye pee ocyc cyc. y oy aae apou, aa oopx xapaepyec ayo, acoo ao.

Moeco ay, aco a aa cnempo paccapaeo y pee.

oooe pecaee caa aaec aco. Bpeeoe acooe pecae caa coepeo aea. Bop oo oo pecae ac o ocoeoce ocao paccapaeo aa.

2.2 OCHOBHE T PEPHX CHAOB.

EPOECE HEPEPBHE CHA oco a peypx cao oocc epoec, o epoec eepoec ca.

epoec ca pecae coo y pee, yoeopy yco f (t) = f (t + T ), (2.1) f(t) T T t Pc. 2.1 pep epoeco y e t o oe pee a epae - < t < ; T eoopa ocoa ae oe poeyo pee, yoeop yco (2.1), aaec epoo y f(t).

epoeca y f(t) oa eca oo peeax poeya pee, paoo epoy T, aee oa ooc oopec a poe aoo epoa.

epoec ca ec eocyec, a a pea ca e oe pooac ecoeo, o ee aao oe. Oao eopeecx cceoax oe epoecoo caa coyec poo ae peya, cooecye aae eceoc.

epoeca y poooo a, yoeopa yco pxe:

opaea ycoo-epepa, ee oeoe co cpeyo a epoe, oe pecaea po Af (t) = + An cos(nt - n ), (2.2) n=e A0 ocoa cocaa, An aya; n = n acoa; n aaa aa n- apo.

Ta opao, epoec ca oo paccapa a peya aoe py a pya ecoeoo oeca apo ocoo cocae.

o epoec ca pecae coo y, cocoy cy apoecx cocax c poo acoa. p ypae e poecco cpeac ca, aco oopx e axoc pocx pax coooex, o peopeee cooae o epoecx cao.

Oco coco ocex ec o a, o x oe opeee pe epo (o epo).

Heepoec cao aaec peyp ca, opeee eepoeco ye, aao peeax oeoo (t1 t t2 ) oyecoeoo (t1 t < ) poeya pee, e f(t) t1 tt Pc. 2.2 pep eepoecoo caa oopoo oa oeceo paa y. opa caa oe paec o.

Heepoec ca oo peca epoeco y-e pee c ecoeo o epoo (pc. 2.2).

Maeaec eo pecae cox cao a epoecx, a eepoecx e cooyoc eeapx apoecx cocax aaec apoec aao.

2.3 PEOPAOBAHE PE, EO OCHOBHE CBOCTBA xapaepc cepo cao coyec peopaoae ype. p peopaoae ype aaec oepaop F(i) = f (t)e-itdt, (2.3) opa peopaoae ype it F(t) = (2.4) F(i)e d.

peopaoae ype ca o aoe cooece a oeca y ( f (t) F(i)) : epoe oeco f(t) y eceoo apyea t; opoe oeco F(i) y oo apyea i. poe peopaoae ype (2.3) ooe o aaoy opay f(t) a eo opaee F(i), opaoe peopaoae (2.4) ooe, aoopo, o aaoy opae F(i) a opa f(t).

Oco coca peopaoa ype c:

1 Coco eoc.

n Ec f (t) = fi (t), o i=n F(i) = (i), (2.5) Fi i=e f(t), f1(t),..., fn(t) eoope y; F(i), F1(i),..., Fn(i) opae cooecyx y.

2 Teopea aaa.

Ec f(t) F(i), o f (t - ) e-i F(i). (2.6) 3 Teopea cee cepa.

Ec f(t) F(i), o ei0 f(t) F(i ( 0)). (2.7) 4 Pa xapaep y f(t).

Ec y f(t) ea, o ee opaee ec eeceo ye, eo ooceo opeeec a F(i) = F() = 2 f (t)costdt. (2.8) Ec y f(t) eea, o ee opaee ec co o ye, eeo ooceo :

F(i) = -i f (t)sin tdt (2.9) Oee oeco coc peopaoa ype opao oe, o eo peee e (2.5) (2.9) coyc p cceoa peypx cao.

2.4 CETP CHAOB a ye o caao, epoec ca pecaec po ype (2.2), cpyypa eo cepa ooc opeeec aya aa apo, .e. oye An apyeo n, n = 1, 2, Cep ay epoecoo caa, coco paoocox , a oopx poopoaa aya An cooecyx apo, pee a pc. 2.3.

An A1 AAA1 2 1 3 Pc. 2.3 Cep epoecoo caa Hepepa pa, coea o cepa, aaec oae cepa ay. Ha pae aco yoa pee oeca opa pa ype:

f (t) = Aneint, (2.10) n=e A oeca aya, n tAn = f (t)e-intdt. (2.11) T t cepa x epoecx cao oo ycao xapaepe coca:

1 Cep cea cpe, o coepa oo apo, aco oopx pa ocoo acoe. Heoope apo oy ocycoa.

2 e oe epo caa T, e ee epa = ey coce T acoa , ceoaeo, "ye" cep. p T oya eepoecy y, cep oopo caoc co, o p o ay yeac.

3 C yeee eoc yco p ocoo epoe ay apo yeac, a cep caoc "ye".

4 Ec c yeee eoc poyox yco yea ayy o aoy A0 =, o x oceoaeoc ye cpec oceoaeoc eaT y, a ay cep ocooy cex aco ae A =.

T eepoecx cao oc oe cnempao nomocmu, oopa pecae coo dA F(i) =, (2.12) d e A ecoeo ae ay eepoeco y, T / A = lim f (t)e-intdt. (2.13) T T -T / Bey F(i) aa ae cepao xapaepco eepoeco y, a oy F(i) = F() cepo.

ocoy cepaa xapaepca oeca ea, o ee oo peca e F(i) = a() + ib() = F()e-i(), b() 2 e a() = f (t)costd ; b() = f (t)sin td ; F() = a() + b() ; () = arctg.

a() - Cpyypa cepa epoecoo caa ooc opeeec oye ao cepao xapaepc.

acoc oy a cepao xapaepc eepoecoo caa aa cooeceo cepo ay cepo a eepoecoo caa.

Ocoeoc cepax coc eepoecoo caa coco ceye:

1 Cep cea epepe xapaepyec ooc ay apo, pxoxc a epa [0; ].

2 p yee eoc yca eo cep pacpec o oc, a ae ooc ay yeac.

3 Ec oopeeo c yeee eoc poyooo yca yea eo ayy o aoy An =, o yc cpec ea-y, a T cepaa ooc ocoo ee, pao ee o ce aaoe aco (-;).

2.5 PACPEEEHE HEP BCETPAX CHAOB B cyae epoecoo caa pe ey o pacpeee ooc eo cepe, oopa opeeec a R R 2 Pcp = A0 + An, (2.14) 4 n=e A0, An oe pa ype cooecyeo epoecoo caa; R copoee eea yaca, epe oop poxo ca.

Pacpeeee ep cepe epoecoo caa pecaec e cy ecoeo ax caaex, cooecyx ecoeo a yaca acooo cepa:

W = (2.15) F() d.

Bpaee F() d pecae coo ep, eey cepa coca caa, pacooe ooce aco d opecoc aco, aaec epeeco cepao ooc eepoecoo caa. opya (2.15) aaec opyo Pe paeco apcea coyec opa acao aco poyca p yco, o ocoe cocae cepa poycac e ee.

2.6 PATECA PHA CETPA CAEH CHAOB p epeae epoecx cao epe peae cce ypae oe epeao opeeeoe oeco apo x ecoeoo ca. p o ao epea apoece cocae c ooceo o aya. B c c oc oe paeco p cepa caa, o oopo oaec oac aco, peeax oopo ea apoece cocae caa c aya, pea aepe aay ey. p ope paeco p cepa caa eoxoo ya peoa cay c epeeco o pe c o pe coxpae eo op.

B cyae eepoecoo caa a e, a cyae epoecoo caa, eaeo epeaa cocae caa co ae aya. C epeeco o pe paeca pa cepa oeaec o oac aco, peeax oopo cocpeooea oaa ac ce ep caa, c o e pe oycx cae op caa opee paecy py cepa e pecaec oo. pecaee o xapaepe cae caa acoc o p cepa oe oyeo p cceoa poxoe cao epe cce c aa xapaepca.

2.7 PECTABEHE CHAOB Ca oy pecae pa opao, p o xoo ca cea ec epep, a pecae oe ca a xoe.

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