Telecommunications Engineering I - Modulation, Multiplexing and Multiple Access
Short Description
Telecommunications Engineering, Modulation, Amplitude modulation (AM), Frequency modulation (FM), Phase modulation (PM),...
Description
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Ykdkcaggujbcetbajs Kjfbjkkrbjf B @arge Okoedebjkj
5;9
Ykdkcaggujbcetbajs Kjfbjkkrbjf B Gaiudetbaj
5;;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Vlet bs gaiudetbaj1 • Vk levk e dawkr-hrkqukjcy sbfjed, sucl es vabck, gusbc ar iete mbts. • Ylbs bs ceddki tlk gaiudetbjf sbfjed (—bjtkddbfkjt sbfjed‗). • Bh wk wejt ta trejsgbt tlbs avkr ebr ar wbrk, wk jkki e hrkqukjcy tlet wbdd prapefetk (trevkd tlraufl) tlbs gkibug. • Ylk sbfjed bs cerrbki aj e cerrbkr wevk. • Sagklaw wk cagmbjk tlk gaiudetbjf sbfjed wbtl tlk cerrbkr wevk ta harg e gaiudetki sbfjed. 5;8
Vlet bs gaiudetbaj •
Bike bs ta clejfk ajk ar gark ah tlk wevkharg peregktkrs – egpdbtuik, plesk, hrkqukjcy
bj e reiba-hrkqukjcy cerrbkr, bj rkspajsk ta tlk sbfjed wk wejt ta trejsgbt. • Bj atlkr waris, wk supkrbgpask ar cagmbjk ajk sbfjed aj ejatlkr. • Ylk trbco bs law ta ia tlbs sa tlet tlk arbfbjed sbfjed cej mk rkcavkrki et tlk rkckbvkr. • Edsa iksbrk – – – –
gbjbged cast/cagpdkxbty, gbjbged pawkr westefk, gexbgug quedbty ah tlk rkcavkrki sbfjed, gbjbgug susckptbmbdbty ta bjtkrhkrkjck (kdkctrbced jabsk eji bjtkrhkrkjck). 5;6
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Yypks ah gaiudetbaj • Ylkrk erk gejy ibhhkrkjt typks ah gaiudetbaj0 – Egpdbtuik gaiudetbaj (EG) clejfks tlk egpdbtuik ah e lbfl hrkqukjcy cerrbkr bj rkspajsk ta tlk daw-hrkqukjcy gaiudetbjf sbfjed? – Hrkqukjcy gaiudetbaj (HG) clejfks tlk hrkqukjcy ah e lbfl hrkqukjcy cerrbkr bj rkspajsk ta tlk daw-hrkqukjcy gaiudetbjf sbfjed? – ^lesk gaiudetbaj (^G) clejfks tlk plesk ah e lbflhrkqukjcy cerrbkr bj rkspajsk ta tlk daw-hrkqukjcy gaiudetbjf sbfjed?
• Edsa tlkrk erk gejy atlkr cagmbjetbajs (usueddy ah egpdbtuik eji plesk), wlbcl fbvk lbflkr tlrauflput (iete retk) har ibfbted iete systkgs. 5;<
Avkrvbkw ah gaiudetbaj
5;2
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
3
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk
58>
!ajckpt ah gaiudetbaj • Ylk sbfjed bs cerrbki aj e cerrbkr wevk. • Sagklaw wk cagmbjk tlk gaiudetbjf sbfjed wbtl tlk cerrbkr wevk ta harg e gaiudetki sbfjed. • Ylkrk erk gejy typks, kf. HG, AHIG (uski bj wbrkdkss jktwaros), UEG (ibfbted gaiudetbaj), ktc. • Ylk gaiudetbaj les ta accur et tlk trejsgbttkr. • Fkttbjf tlk gaiudetbjf (euiba) sbfjed meco aut ah tlk gaiudetki (reiba) sbfjed bs ceddki ikgaiudetbaj.
585
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
9
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Gaiudetbaj typks • Egpdbtuik Gaiudetbaj bs wlkrk wkgaiudetbjf clejfk tlksbfjed. egpdbtuik ah tlk cerrbkr (EG) eccaribjf ta tlk • Hrkqukjcy Gaiudetbaj (HG) bs wlkrk wk clejfk tlk hrkqukjcy ah tlk cerrbkr eccaribjf ta tlk gaiudetbjf sbfjed. • ^lesk Gaiudetbaj (^G) bs wlkrk wk clejfk tlk plesk ah tlk cerrbkr eccaribjf ta tlk gaiudetbjf sbfjed.
58=
"G# $G eji %G
583
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Vly edd tlk ibhhkrkjt typks1 •
EG usks sbgpdk kdkctrajbcs. – [ski sbjck kerdy 52>>‒s, ehtkr tkdkfrepl kre. – EG uski har ejedaf tkrrkstrbed
•
HG bs jat es susckptbmdk ta jabsk. – Kdkctrajbcs bs e mbt g ark cagpdbcetki (kspkcbeddy bj rkckbvkr). – HG uski har setkddbtk (mkceusk bt‒s dkss ehhkctki my tlk etgasplkrk), sagk tkdkgktry systkgs (rkgatk cajtrads).
•
^G wes jat uski gucl ujtbd wk jkkiki bt har ibfbted trejsgbssbaj. • Ibfbted gaiudetbaj usks e cagmbjetbaj ah EG eji ^G ta fkt lbfl mbtretks. – Ykcljadafy bs gucl gark cagpdkx tlej sbgpdk EG ar ^G.
589
"gpdbtuik gaiudetbaj • Vk edsa jkki ta tlbjo ah tlk rkckbvkr, wlkj wk iksbfj tlk trejsgbttkr. • Mesbceddy, tlk rkckbvkr jkkis ta strbp ewey tlk lbflkr hrkqukjcy (cerrbkr) et ]H, eji dkevk tlk euiba (EH). • Vlet bh wk gudtbpdy tlk gaiudetbjf euiba my tlk reiba hrkqukjcy cerrbkr1 • Ylk rkckbvkr wbdd jkki ta ojaw tlk cerrbkr hrkqukjcy, sa wk eii e mbt ah tlet bj ta tlk wevkharg.
58;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
8
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"gpdbtuik gaiudetbaj & Getlkgetbceddy • Dkt tlk cerrbkr mk
• Ylk gaiudetbaj bs g(t). – Ylbs bs usueddy euiba, caudi mk vbika ar iete.
• Ya geok tlk Egpdbtuik Gaiudetki (EG) wevkharg, gudtbpdy eji eii
• Jatk0 Ylk cagpajkjt perts ah tlbs, g(t)sbj ςct eji Ec sbjςct • Jatk wlet tlk kquetbaj bs iabjf. 588
"gpdbtuik gaiudetbaj & 'befreg
586
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
6
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"gpdbtuik gaiudetbaj & Vevkhargs Vevkhargs cagmbjki har stejieri egpdbtuik gaiudetbaj
Jatk0 Vk levk uski cerrbkr wevkharg sbjςct. Gejy rkhkrkjcks usk e casbjk wevk bjstkei. Bt iaks jat gettkr, `ust clejfks tlk getls e mbt.
58<
"gpdbtuik gaiudetbaj & Vevkhargs • Jatk law tlk cerrbkr bs e lb flkr hrkqukjcy. – Bt bs edweys sbjk (ar casbjk)
• Vk levk slawj tlk gaiudetbaj es e sbjk wevk. – Sbjk (ar casbjk) bs AO har e tkst sbfjed.
• sbfjed Mut bjdbok prectbck, jatstrkeg sbjk mut e cagpdkx vabck,gaiudetbaj vbika, ar e bs iete (5‒s eji >‒s rkprkskjtki my lbfl eji daw vadtefks, b.k., squerk wevk) • Bj prectbck tlk cerrbkr bs e gucl lbflkr hrkqukjcy.
582
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"gpdbtuik gaiudetbaj & Vevkhargs Cerrbkr wbtl sbjfdk-tajk gaiudetbaj
56>
Kjvkdapk Egpdbtuik Gaiudetbaj – Ylk kjvkdapk ah tlk wevkharg
565
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
2
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"gpdbtuik gaiudetbaj & "jedysbs • Vk jkki ta ojaw e hkw tlbjfs emaut tlbs EG-wevkharg. • Vlet erk tlk hrkqukjcy cagpajkjts tlet wk kji up wbtl1 – Ylbs bs bgpartejt har tlk clejjkd mejiwbitl, sa skvkred clejjkds cej ca-kxbst eji jat bjtkrhkrk wbtl kecl atlkr.
• Vk waudi dbok ta mk emdk ta waro aut tlk peregktkrs ah tlk wevkharg • Edsa wk waudi dbok ta ojaw law gucl pawkr tlk trejsgbttkr jkkis. • Vk stert aur ejedysbs wbtl e pdebj sbjk wevk tkst sbfjed.
56=
"G(ejedysbs
563
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"G(ejedysbs
569
"G(ejedysbs
56;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
55
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"G(ejedysbs EG wevkharg slawbjf M es gexbgug ah kjvkdapk, eji E es gbjbgug
568
"jedysbs
566
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"jedysbs
Law ia wk waro aut tlk Ec eji Eg 1
56<
"jedysbs
562
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
53
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Khhkct ah gaiudetbaj bjik Clejfbjf gaiudetbaj bjikx
Lbflkr », egpdbtuik clejfk gark prajaujcki.
5
$rk)ukjcy ejedysbs • Vlet erk tlk hrkqukjcy cagpajkjts ah tlbs EG wevkharg1 • Ylbs bs bgpartejt ta ojaw, sbjck bt tkdds us law wbik tlk clejjkd jkkis ta mk. • Ar kqubvedkjtdy, law gejy clejjkds wk cej hbt bj e fbvkj spkctrug eddacetbaj.
5 %lesk gaiudetbaj ^G sbfjed har gaiudetbaj g(t) bs
Cagperk wbtl
wlkrk ϛ bs `ust e plesk ejfdk. Bh bt bs hbxki, wk `ust wrbtk ϛ. Mut bh bt clejfks avkr tbgk, wk wrbtk bt es ϛ(t). ^G 7 Clejfk tlk plesk ϛ bj tlk cerrbkr kquetbaj.
=>;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
=8
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'befreg> %lesk gaiudetbaj ^lesk gaiudetbaj
=>8
$rk)ukjcy eji plesk Hrkqukjcy gaiudetbaj eji plesk gaiudetbaj erk sbgbder. Hrkqukjcy kqueds retk ah clejfk ah plesk
Getlkgetbceddy,
^lesk bs tlk sug ah hrkqukjcy clejfks =>6
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
=6
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'khbjbtbaj> $rk)ukjcy gaiudetbaj • •
Hrkqukjcy gaiudetbaj eji plesk gaiudetbaj erk sbgbder. Vk lei kerdbkr
wlkrk bjstejtejkaus hrkqukjcy bsςb(t) • Sa tlk hrkqukjcy bs tlk pert bj tlk squerk mrecokts, bk. ςc + ohg(t) • HG 7 Clejfk tlk hrkqukjcy ς bj tlk cerrbkr kquetbaj.
=><
$rk)ukjcy gaiudetbaj Jaw rkgkgmkr tlet hrkqukjcy kqueds retk ah clejfk ah plesk,
ar turjki erauji plesk bs tlk bjtkfred ah hrkqukjcy,
Sa hrag
wk caudi bjtkfretk tlk ςb(t) pert. Bt caudi mk wrbttkj es =>2
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
=<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$rk)ukjcy gaiudetbaj
=5>
Ybgk wevkhargs Hrkqukjcy eji ^lesk gaiudetbaj
=55
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
=2
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$G & "jedysbs HG sbfjed har gaiudetbaj g(t) bs
har e sbjfdk-tajk sbjusabi gaiudetbaj
Ylk HG sbfjed mkcagks
wbtl
=5= Jatk0 Ylbs bs ajdy har e sbjfdk-tajk gaiudetbaj. Bj rkedbty tlk gaiudetbaj bs e cagpdkx sbfjed, mut har ejedysbs wk usk e sbjfdk tkst tajk.
$G & "jedysbs Sbjfdk-tajk HG sbfjed
Vk cedd ν tlk ikvbetbaj retba, ikhbjki es
=53
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
3>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$G & "jedysbs Sbjfdk-tajk HG sbfjed
Hrkqukjcy cagpajkjts cej mk hauji bj tkrgs ah Mksskd hujctbajs ta mk
Ylk Mksskd hujctbaj @o(ν ) bs uski, wlkrk o bs tlk hrkqukjcy cagpajkjt eji ν bs tlk ikvbetbaj retba ar tlk gaiudetbaj bjikx.
=59
$G & "jedysbs • [sk Mksskd temdks ar cagputkr eji waro aut tlk egpdbtuiks ah tlk hrkqukjcy cagpajkjts. • Freplbced bjtkrprktetbaj0 irew e dbjk et tlk gaiudetbaj bjikx aj tlk Mksskd hujctbaj pdat eji rkei ahh egpdbtuiks ah lergajbcs. • ]kgkgmkr tlet lergajbcs erk aj kbtlkr sbik ah tlk cerrbkr, bk., bt bs syggktrbced.
=5;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
35
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
.ksskd hujctbajs ah tlk hbrst obji @j,νGaiudetbaj bjikx ν
=58
.ksskd hujctbajs @j,νGaiudetbaj Bjikx ν
=56
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
3=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk ∝ Khhkct ah ν
ν75
=5<
Kegpdk ∝ Khhkct ah ν
ν7=
=52
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
33
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk ∝ Khhkct ah ν
ν79
==>
$G & "jedysbs Law bs tlk pawkr ibstrbmutki bj tlk sbikmejis1 ^awkr bs prapartbajed ta tlk gefjbtuik ah tlk cagpajkjt squerki. Jatk edsa tlet
==5
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
39
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Ykdkcaggujbcetbajs Kjfbjkkrbjf B 'bfbted gaiudetbaj
Gaiudetbaj •
Ibfbted gaiudetbaj – ibfbted iete bs trejsdetki bjta ej ejedaf sbfjed (meskmeji) – ESO, HSO, ^SO – ibhhkrkjcks bj spkctred khhbcbkjcy, pawkr khhbcbkjcy, ramustjkss
•
Ejedaf gaiudetbaj
•
Gatbvetbaj
– slbhts ckjtkr hrkqukjcy ah meskmeji sbfjed up ta tlk reiba cerrbkr – sgeddkr ejtkjjes (k.f., ο/9) – Hrkqukjcy Ibvbsbaj Gudtbpdkxbjf – gkibug clerectkrbstbcs
•
Mesbc sclkgks – Egpdbtuik Gaiudetbaj ( EG) – Hrkqukjcy Gaiudetbaj ( HG) – ^lesk Gaiudetbaj ( ^G)
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
3;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Gaiudetbaj eji ikgaiudetbaj ibfbted iete =3==3=33=
ejedaf +esk+eji sbfjed
ibfbted gaiudetbaj
ejedaf gaiudetbaj
reiba trejsgbttkr
reiba cerrbkr
ejedaf ikgaiudetbaj
ejedaf +esk+eji sbfjed
syjclrajb5etbaj ikcbsbaj
ibfbted iete =3==3=33=
reiba rkckbvkr
reiba cerrbkr
'bfbted gaiudetbaj • Yrejsgbttbjf ibfbted (mbjery) sbfjeds • Jkki ta kjcaik > eji 5 strkegs skrbeddy • Ibstbjfubsl0 – ^essmeji0 gaiudetk ajta e cerrbkr. – Meskmeji0 kjcaik >/5 ibrkctdy wbtl ja cerrbkr.
==;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
38
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted gaiudetbaj & Ylkarktbced dbgbts • Law ia wk gexbgbzk tlk jugmkr ah mbts pkr skcaji (omps, Gmps, Fmps)1 • Ikpkjis aj0 – Law wk kjcaik kecl mbt – Egaujt ah jabsk bj tlk clej jkd (kf., tkdkplajk dbjk, aptbc hbmkr, reiba)
==8
!lejjkd cepecbty ,9y)ubst(;ertdkyGexbgug iete retk (cepecbty) ikpkjis aj mejiwbitl. Meski aj Jyqubst retk (pudsks bj skcaji ≩ =M), cepecbty bj mbts pkr skcaji usbjf clejjkd mejiwbitl M wbtl G dkvkds pkr sygmad bs
M G
mps
Mejiwbitl ah tlk clejjkd (Lz) Jugmkr ah dkvkds uski har kecl sbfjedbjf kdkgkjt Mbts pkr skcaji
==6
Jatk0 daf bs ta mesk =, mkceusk bt bs mbjery bjhargetbaj
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
36
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk> %*Y9 8 %u+dbc *wbtclki Ykdkplajk 9ktwaro Edsa ceddki —^AYS‗ 7 —^debj Adi Ykdkplajk Systkg‗ Mejiwbitl M ~ 3oLz Vbtl ajk mbt pkr sbfjeddbjf bjtkrved (—sygmad‗) G 7 = [sbjf C 7 =M daf=G, C 7 =∖3>>>∖5 7 8 omps Ya fkt e lbflkr retk, wk jkki derfkr G (mbts pkr sygmad)
==<
!lejjkd cepecbty 6 jabsk Gexbgug iete retk (cepecbty) ikpkjis aj jabsk – Slejjaj-Lertdky Dew. Cepecbty bj mbts pkr skcaji wbtl fbvkj clejjkd mejiwbitl M, SJ] S/J eji usbjf wlbtk jabsk essugptbaj bs
M S J
mps
Mejiwbitl ah tlk clejjkd (Lz) Sbfjed ^awkr (V) Jabsk ^awkr (V) Mbts ^kr Skcaji ==2
Jatk0 Lkrk S/J bs jat kxprksski bj iM
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
3<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk> %*Y92%AY* Suppask S/J 7 5>>>, M 7 3 oLz SJ] 7 5>daf5>5>3 7 3> iM Vlet bs tlk cepecbty1 [sbjf C 7 M daf=(5 + S/J) C 7 3>>> ∖daf=(5 + 5>>>) ≌ 3>>> ∖ 5> 7 3>omps
Ylk prkskjck ah jabsk rkiucks tlk cepecbty.
=35
Jatk0 =5> 7 5>=9, sa daf ta mesk = ah 5>>> bs epprax. 5>.
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
32
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted gaiudetbaj • Ya kjcaik > ar 5, wk caudi `ust clejfk ajk ah egpdbtuik, hrkqukjcy ar plesk • Ajdy jkki = dkvkds. – Ibfbted Cerrbkr Gaiudetbaj – Egpdbtuik – Ibfbted Cerrbkr Gaiudetbaj – Hrkqukjcy – Ibfbted Cerrbkr Gaiudetbaj – ^lesk
=3=
'bfbted gaiudetbaj •
Gaiudetbaj ah ibfbted sbfjeds ojawj es slbht okybjf
•
Egpdbtuik Slbht Okybjf ( ESO)0
5
>
5
– vkry sbgpdk – daw mejiwbitl rkqubrkgkjts t
– vkry susckptbmdk ta bjtkrhkrkjck •
Hrkqukjcy Slbht Okybjf ( HSO)0
5
>
5
– jkkis derfkr mejiwbitl t
•
^lesk Slbht Okybjf ( ^SO)0
5
>
5
– gark cagpdkx – ramust efebjst bjtkrhkrkjck
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
t
9>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted cerrbkr gaiudetbaj & "gpdbtuik Egpdbtuik gaiudetbaj ah mbjery sbfjed
=39
'bfbted cerrbkr gaiudetbaj & $rk)ukjcy Hrkqukjcy gaiudetbaj ah mbjery sbfjed
=3;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
95
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted cerrbkr gaiudetbaj & %lesk ^lesk gaiudetbaj ah mbjery sbfjed
=38
'bfbted gudtb(dkvkd gaiudetbaj • Ya fkt lbflkr tlrauflput, wk caudi kjcaik skvkred mbts et ajck • Kjcaik twa mbts tafktlkr (ceddki e ibmbt) – es 9 ibstbjct egpdbtuik dkvkds ar – es 9 ibstbjct hrkqukjcbks ar – es 9 ibstbjct plesks
=36
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
9=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted cerrbkr gaiudetbaj & Gudtb(dkvkd "G Egpdbtuik gaiudetbaj ah gudtb-dkvkd mbjery sbfjed
=3<
'bfbted cerrbkr gaiudetbaj & Gudtb(dkvkd $G Hrkqukjcy gaiudetbaj ah gudtb-dkvkd mbjery sbfjed
=32
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
93
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted gaiudetbaj • Kvkj lbflkr tlrauflput, kjcaik gudtbpdk cagmbjetbajs ah egpdbtuik eji plesk. • U^SO – Uueireturk ^lesk Slbht Okybjf. – Gudtbpdk plesk ejfdks eddawki
• UEG – Uueireturk Egpdbtuik Gaiudetbaj. – Clejfks matl plesk eji egpdbtuik.
=9>
'bfbted cerrbkr gaiudetbaj & 0%*O Uueireturk ^lesk Slbht Okybjf
=95
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
99
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted cerrbkr gaiudetbaj & 0"G Uueireturk Egpdbtuik Gaiudetbaj
=9=
"ivejcki $*O • Mejiwbitl jkkiki har HSO ikpkjis aj tlk ibstejck mktwkkj tlk cerrbkr hrkqukjcbks • Spkcbed prk-cagputetbaj evabis suiikj plesk slbhts ⇝ GSO (Gbjbgug Slbht Okybjf) – mbt skperetki bjta kvkj eji aii mbts, tlk iuretbaj ah kecl mbt bs iaumdki – ikpkjibjf aj tlk mbt veduks (kvkj, aii) tlk lbflkr ar dawkr hrkqukjcy, arbfbjed ar bjvkrtki bs claskj – tlk hrkqukjcy ah ajk cerrbkr bs twbck tlk hrkqukjcy ah tlk atlkr • Kvkj lbflkr mejiwbitl khhbcbkjcy usbjf e Feussbej daw-pess hbdtkr ⇝ FGSO (Feussbej GSO), uski bj FSG
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
9;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk ah G*O =
3
=
=
3
=
3
iete
+bt kvkj
3=3=
kvkj +bts
aii
33==
aii +bts
sbfjed veduk
lj jl (( ??
daw hrk)ukjcy
l> lbfl hrk)ukjcy j> daw hrk)ukjcy ?> arbfbjed sbfjed (> bjvkrtki sbfjed
lbfl hrk)ukjcy
G*O sbfjed
t 9a plesk slbhts4
Yaweris lbflkr tlrauflput • ^eco gark eji gark mbts bjta kecl sygmad bjtkrved • Ylk “U‒ gkejs Uueireturk – wk cej fkjkretk tlksk wevkhargs hrag sbjk eji casbjk eiiki tafktlkr • Uueireturk gkejs 2> ¾ plesk.
=9;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
98
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
"ivejcki %*O •
– – – – –
•
mbt veduk >0 sbjk wevk mbt veduk 50 bjvkrtki sbjk wevk vkry sbgpdk ^SO daw spkctred khhbcbkjcy ramust, uski k.f. bj setkddbtk systkgs
=
=3
B
3
0
==
U^SO (Uueireturk ^lesk Slbht Okybjf)0 – = mbts caiki es ajk sygmad – sygmad iktkrgbjks slbht ah sbjk wevk – jkkis dkss mejiwbitl cagperki ta M^SO – gark cagpdkx
•
0
M^SO (Mbjery ^lesk Slbht Okybjf)0
B
33
3=
"
Ahtkj edsa trejsgbssbaj ah rkdetbvk, jat emsadutk plesk slbht0 IU^SO Ibhhkrkjtbed U^SO
t ==
=3
33
3=
0ueireturk "gpdbtuik Gaiudetbaj • Uueireturk Egpdbtuik Gaiudetbaj ( UEG) – cagmbjks egpdbtuik eji plesk gaiudetbaj – bt bs passbmdk ta caik j mbts usbjf ajk sygmad – =j ibscrktk dkvkds, j7= bikjtbced ta U^SO • Mbt krrar retk bjcrkesks wbtl j, mut dkss krrars cagperki ta 0 33=3 cagperemdk ^SO sclkgks – Kxegpdk0 58-UEG (9 mbts 7 5 sygmad) – Sygmads >>55 eji >>>5 levk tlk segk plesk ψ, mut ibhhkrkjt egpdbtuik e, sygmads >>>> eji 5>>> levk ibhhkrkjt plesk, mut segk egpdbtuik.
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
33==
333= 3333
7 e
B =333
96
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
;bkrerclbced gaiudetbaj • • • • •
IXM-Y gaiudetks twa skperetk iete strkegs ajta e sbjfdk IXM-Y strkeg Lbfl ^rbarbty (L^) kgmkiiki wbtlbj e Daw ^rbarbty (D^) strkeg Gudtb cerrbkr systkg, emaut =>>> ar >> cerrbkrs U^SO, 58 UEG, 89UEG Kxegpdk0 89UEG – faai rkckptbaj0 rksadvk tlk kjtbrk U 89UEG cajstkddetbaj – paar rkckptbaj, gambdk rkckptbaj0 rksadvk ajdy U^SO partbaj – 8 mbt pkr UEG sygmad, = gast 5> sbfjbhbcejt iktkrgbjk U^SO – L^ skrvbck caiki bj U^SO (= mbt), D^ usks rkgebjbjf 9 mbt
B
>> >>>>5>
>5>5>5
'bfbted kjcaibjf & .esk+eji • Meskmeji0 ja cerrbkr es sucl – Kf., Gejclkstkr uski aj Ktlkrjkt 5>Gmps (mps 7 mbts pkr skcaji). • Xerbetbajs har lbflkr retks (5>>Gmps, 5Fmps, ...)
• Hujiegkjted pramdkg0 jkki ta iktkct wlkrk e mbt sterts eji staps. • ]kckbvkr jkkis ta okkp treco ah plesk, ta waro aut wlkrk mbts stert eji kji • Kjcaibjf gkejs tlet e dajf strbjf ah >‒s ar 5‒s iaj‒t ceusk rkckbvkr ta dask syjclrajbzetbaj • =92
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
9<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'bfbted kjcaibjf & Gejclkstkr kjcaibjf Kjcaiks > es D-L trejsbtbaj Kjcaiks 5 es L-D trejsbtbaj Gejclkstkr kjcaibjf
=;>
'bfbted kjcaibjf & .esk+eji • ]kckbvkr jkkis ta okkp treco ah plesk, ta waro aut wlkrk mbts stert eji kji • Kjcaibjf gkejs tlet e dajf strbjf ah >‒s ar 5‒s iaj‒t ceusk rkckbvkr ta dask syjclrajbzetbaj • ]kckbvki wevkhargs erk jat pkrhkct • Squerk kifks ojacoki ahh iuk ta clejjkd hbdtkrbjf khhkcts (cepecbtejck/bjiuctejck) • Gey edsa levk jabsk caupdki bj =;5
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
92
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
:kckbvki wevkhargs ]kckbvki wevkhargs erk jat pkrhkct. Squerk kifks ojacoki ahh iuk ta clejjkd hbdtkrbjf khhkcts (cepecbtejck/bjiuctejck) Gey edsa levk jabsk caupdki bj
Gejclkstkr wevkhargs ehtkr fabjf tlraufl sbgpdk tlkarktbced clejjkd
=;=
*uggery • Gaiudetbaj supkrbgpasks gaiudetbaj aj cerrbkr. • Ylkrk erk gejy ibhhkrkjt typks ah gaiudetbaj. • Gaiudetbaj bssuks bjcduik cagpdkxbty ah trejsgbttkr, cagpdkxbty ah rkckbvkr, mejiwbitl rkqubrki, bggujbty ta jabsk, ktc. • Spkctrug ikpkjis aj typk ah gaiudetbaj. • Squkkzk gark mbts pkr skcaji my kxpdabtbjf cagmbjetbajs ah egpdbtuik eji plesk. =;3
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Ykdkcaggujbcetbajs Kjfbjkkrbjf B Gudtbpdkbjf eji Gudtbpdk "cckss
=;9
'khbjbtbaj eji passb+bdbtbks
=;;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;5
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Gudtbpdkbjf • Gudtbpdkxbjf bj 9 ibgkjsbajs – speck (s b)
clejjkds ob o5
– tbgk (t)
o=
o3
o9
o;
o8
c
– hrkqukjcy (h)
t
c t
– caik (c) s5
h s=
• Faed0 gudtbpdk usk ah e slerki gkibug
h
c t
• Bgpartejt0 fueri specks jkkiki!
s3
h
$rk)ukjcy gudtbpdkbjf • Skperetbaj ah tlk wladk spkctrug bjta sgeddkr hrkqukjcy mejis • E clejjkd fkts e ckrtebj meji ah tlk spkctrug har tlk wladk tbgk • Eivejtefks – ja iyjegbc caaribjetbaj o5
jkckssery – waros edsa har ejedaf sbfjeds
o=
o3
o9
o;
o8
c h
• Ibseivejtefks – westk ah mejiwbitl bh tlk trehhbc bs ibstrbmutki ujkvkjdy t – bjhdkxbmdk
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$'G> %rbjcbpdk Kecl clejjkd cerrbki aj ibhhkrkjt hrkqukjcy
=;<
$'G> !errbkr wevks
=;2
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;3
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$'G Cerrbkr et ibhhkrkjt hrkqukjcbks. Gaiudetbaj cej mk ejytlbjf
=8>
$'G> *u+(clejjkds Hbdtkr rkspajsks Jaclejjkdavkrdep
Clejjkdsavkrdep
=85
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;9
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$rk)ukjcy(ibvbsbaj gudtbpdkbjf
=8=
$'G systkg
=83
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!agpasbtk sbfjed
=89
Kegpdk> *tkrka $G
=8;
Jatk0 Cagpetbmbdbty bs usueddy jkkiki bj upfreiks, k.f., mdeco eji wlbtk YX ⇝ cadaur YX
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;8
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*tkrka trejsgbttkr
=88
*tkrka $G spkctrug
=86
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;6
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*tkrka $G rkckbvkr
=8<
*u+cerrbkr systkg
=82
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*u+cerrbkr systkg
=6>
:'* eji :.'*
=65
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
;2
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*u+sbibery !aggujbcetbajs "utlarbty ,*!"- skrvbcks
=6=
!agpdktk $G trejsgbttkr
=63
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
8>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!agpdktk $G rkckbvkr
=69
Artlafajed $'G eppraecl
=6;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
85
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Artlafajed $'G eppraecl ? plesk )ueireturk
=68
Artlafajed $rk)ukjcy 'bvbsbaj Gudtbpdkbjf ,A$'GArtlafajedsbfjeds
Jaj-artlafajedsbfjeds
=66
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
8=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
A$'G •
Gudtbpdy eji bjtkfretk. AHIG rkcavkry
– Cdaco syjclrajbzetbaj jat slawj.
• • •
•
Bh kqued ⇝ fkt e derfkr praiuct Bh jat kqued ⇝ daw (bikeddy zkra) praiuct Bh edd bjput hrkqukjcbks erk artlafajed, tlky wbdd ybkdi zkra har edd daced hrkqukjcbks jat kqued ta tlk daced ajk. Ylus sbfjeds cej mk rkcavkrki, eji cej cakxbst.
=6<
Ybgk ibvbsbaj gudtbpdkbjf ,Y'G• E clejjkd fkts tlk wladk spkctrug har e ckrtebj egaujt ah tbgk • Eivejtefks – ajdy ajk cerrbkr bj tlk gkibug et ejy tbgk – tlrauflput lbfl kvkj har gejy uskrs
o5
o=
o3
o9
o;
o8
c h
• Ibseivejtefks – prkcbsk syjclrajbzetbaj jkckssery t
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
83
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Y'G eji $'G • Cagmbjetbaj ah YIG eji HIG • E clejjkd fkts e ckrtebj hrkqukjcy meji har e ckrtebj egaujt ah tbgk • Kxegpdk0 FSG • Eivejtefks
o5
– mkttkr pratkctbaj efebjst teppbjf (kevksirappbjf)
o=
o3
o9
o;
o8
c
– pratkctbaj efebjst hrkqukjcy skdkctbvk bjtkrhkrkjck
h
• mut0 prkcbsk caaribjetbaj rkqubrki t
*peck 'bvbsbaj Gudtbpdkbjf> !kdd structurk •
Bgpdkgkjts speck ibvbsbaj gudtbpdkx (SIG)
•
Gambdk stetbajs caggujbcetk ajdy vbe tlk mesk stetbaj
•
Eivejtefks ah c kdd structurks
– mesk stetbaj cavkrs e ckrtebj trejsgbssbaj erke (ckdd)
– lbflkr cepecbty, lbflkr j ugmkr ah usk rs – dkss trejsgbssbaj pawkr jkkiki – gark ramust, ikckjtredbzki – mesk stetbaj ikeds wbtl bjtkrhkrkjck, trejsgbssbaj erke ktc. daceddy
•
^ramdkgs – hbxki jktwaro jkkiki har tlk mesk stetbajs – lejiavkr (clejfbjf hrag ajk ckdd ta ejatlkr) jkckssery – bjtkrhkrkjck wbtl atlkr ckdds
•
Ckdd sbzks hrag 45>> g bj cbtbks ta, k.f., 3; og aj tlk caujtry sbik (FSG) kvkj dkss har lbflkr hrkqukjcbks
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
89
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$rk)ukjcy rkusk • •
Hrkqukjcy rkusk ajdy wbtl e ckrtebj ibstejck mktwkkj tlk mesk stetbajs Stejieri gaikd usbjf 6 hrkqukjcbks0 h hE
•
•
hN h= hM
hE hC hI
hM
hN
h
h=
Hbxki hrkqukjcy essbfjgkjt0 – ckrtebj hrkqukjcbks erk essbfjki ta e ckrtebj ckdd – pramdkg0 ibhhkrkjt trehhbc daei bj ibhhkrkjt ckdds Iyjegbc hrkqukjcy essbfjgkjt0 – mesk stetbaj claasks hrkqukjcbks ikpkjibjf aj tlk hrkqukjcbks edrkeiy uski bj jkbflmar ckdds – gark cepecbty bj ckdds wbtl gark trehhbc – essbfjgkjt cej edsa mk mesk i aj bjtkrhkrkjck gkesurkgkjts
$rk)ukjcy rkusk hE h= hM hE
hM hE h=
hE h= hM hE
hM hE h=
hE
hM
h=
h
hM
E ckdd cdustkr
hE
hN h=
hE
hM
hC
hE hC hI hN
hM h hE
hI hN h= hM
I ckdd cdustkr
hM hM hM h= h l h= h lM h= hE E E M fM l= lE fM l= lE fM f= f f= f= f fE E E
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
E ckdd cdustkr wbtl E skctar ejtkjjes
8;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!aik ibvbsbaj gudtbpdkbjf ,!'G• Kecl clejjkd les e ujbquk caik
o5
o=
o3
• Edd clejjkds usk tlk segk spkctrug et tlk segk tbgk
o9
o;
o8
c
• Eivejtefks – mejiwbitl khhbcbkjt – ja caaribjetbaj eji syjclrajbzetbaj jkckssery
h
– faai pratkctbaj efebjst bjtkrhkrkjck eji teppbjf
• Ibseivejtefks – verybjf uskr iete retks
t
– gark cagpdkx sbfjed rkfkjkretbaj
• Bgpdkgkjtki usbjf sprkei spkctrug tkcljadafy
9atk> !kdd +rketlbjf • CIG systkgs0 ckdd sbzk ikpkjis aj currkjt daei • Eiibtbajed trehhbc eppkers es jabsk ta atlkr uskrs • Bh tlk jabsk dkvkd bs taa lbfl ckdd sbzk bs ikcrkeski (bj atlkr waris —kxckss uskrs‗ erk irappki aut ah ckdd.
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
88
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*u+deykrs ah 'ete =
!aik 'bvbsbaj Gudtbpdk "cckss ,!'G"• Caik ibvbsbaj gudtbpdk ecckss (CIGE) bs e clejjkd ecckss gktlai utbdbzki my verbaus reiba caggujbcetbaj. • CIGE kgpdays sprkei-spkctrug tkcljadafy eji e spkcbed caibjf sclkgk (wlkrk kecl trejsgbttkr bs essbfjki e caik) ta eddaw gudtbpdk uskrs ta mk gudtbpdkxki avkr tlk segk plysbced clejjkd. • CIGE bs e harg ah sprkei-spkctrug sbfjedbjf, sbjck tlk gaiudetki caiki sbfjed les e gucl lbflkr mejiwbitl tlej tlk iete mkbjf caggujbcetki.
3>3
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
6;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!aik('bvbsbaj Gudtbpdk "cckss ,!'G"• Caik-ibvbsbaj gudtbpdk ecckss (CIGE) wes bjvkjtki skvkred ikceiks efa. • ]kckjt eivejcks bj kdkctrajbcs levk hbjeddy geik bts bgpdkgkjtetbaj kcajagbceddy passbmdk. • CIGE ibhhkrs hrag HIGE mkceusk ajdy ajk clejjkd accupbks tlk kjtbrk mejiwbitl ah tlk dbjo. • Bt ibhhkrs hrag YIGE mkceusk edd stetbajs cej skji iete sbgudtejkausdy? tlkrk bs ja tbgkslerbjf.
3>9
*prkei spkctrug tkcljb)uk • ^ramdkg ah reiba trejsgbssbaj0 hrkqukjcy ikpkjikjt heibjf cej wbpk aut jerraw meji sbfjeds har iuretbaj ah tlk bjtkrhkrkjck • Sadutbaj0 sprkei tlk jerraw meji sbfjed bjta e mraei meji sbfjed usbjf e spkcbed caik – pratkctbaj efebjst jerraw meji bjtk rhkrkjck p a w k r bjtkrhkrkjck
sprkei sbfjed
p awk r iktkctbaj et rkckbvkr h
sbfjed sprkei bjtkrhkrkjck
h
• Sbik khhkcts0 – cakxbstkjck ah skvkred sbfjeds wbtlaut iyjegbc caaribjetbaj – tep-praah • Edtkrjetbvks0 Ibrkct Skqukjck (IS), Hrkqukjcy Lappbjf (HL)
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
68
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*prkei *pkctrug • Vlet cej mk febjki hrag epperkjt westk ah spkctrug1 – Bggujbty hrag verbaus objis ah jabsk eji gudtbpetl ibstartbaj
– Cej mk uski har lbibjf eji kjcryptbjf sbfjeds – Skvkred uskrs cej bjikpkjikjtdy usk tlk segk lbflkr mejiwbitl wbtl vkry dbttdk bjtkrhkrkjck
3>8
Khhkcts ah sprkeibjf eji iksprkeibjf wbtl bjtkrhkrkjck i%2ih b-
i%2ih uskr sbfjed +raei+eji bjtkrhkrkjck jerraw+eji bjtkrhkrkjck
bbh skjikr i%2ih
bbb-
h i%2ih
i%2ih bvh rkckbvkr
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
vh
h
66
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*prkeibjf eji hrk)ukjcy skdkctbvk heibjf clejjkd )uedbty
=
M
N
E
C
jerraw+eji clejjkds
hrk)ukjcy jerraw +eji sbfjed
fueri speck
clejjkd )uedbty
=
M
M
M
M
M
sprkei spkctrug clejjkds
hrk)ukjcy
sprkei spkctrug
*prkei spkctrug • Bjstkei ah trejsgbttbjf aj ajk ar e hkw hrkqukjcbks, tlk gaiudetar ikdbmkretkdy trbks ta usk e gucl wbikr clejjkd mejiwbitl. • Bt bs uski0 – gbdbtery caggujbcetbajs, – ckdduder caggujbcetbajs (wlkrk tlk tkrg CIGE bs uski), – bjtkrhkrkjck-prajk kjvbrajgkjts
• Ywa gebj typks0 – Hrkqukjcy Lappbjf eji – Ibrkct Skqukjck
3>2
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
6<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*prkei spkctrug & Vly1 • Gbdbtery usk0 Vejt ta – Okkp aur trejsgbssbajs skcrkt hrag kjkgy. – Stap kjkgy `eggbjf aur trejsgbssbajs wbtl lbfl-pawkr ]H.
• Cbvbdbej usk0 Vejt ta – Gbjbgbzk khhkct ah bjtkrhkrkjck hrag atlkrs. – Gbjbgbzk aur bjtkrhkrkjck aj atlkrs. – Slerk mejiwbitl wbtl atlkrs (bjstkei ah YIGE ar HIGE).
• Gambdk caggujbcetbajs erk e mbf i rbvkr. 35>
*prkei(spkctrug gudtbpdk ecckss • • • • • •
•
Ylk arbfbjs ah sprkei spkctrug erk bj gbdbtery hbkdi eji jevbfetbaj systkgs. Ykcljbquks ikvkdapki ta caujtkrect bjtkjtbajed `eggbjflevk edsa pravki subtemdk har caggujbcetbaj tlraufl ibspkrsbvk clejjkds bj ckdduder eppdbcetbajs. Bj CIGE kecl uskr bs essbfjki e ujbquk caik skqukjck bt usks ta kjcaik bts bjhargetbaj-mkerbjf sbfjed. Ylk rkckbvkr, ojawbjf tlk caik skqukjcks ah tlk uskr, ikcaiks e rkckbvki sbfjed ehtkr rkckptbaj eji rkcavkrs tlk arbfbjed iete. Ylbs bs passbmdk sbjck tlk crass-carrkdetbajs mktwkkj tlk caik ah tlk iksbrki uskr eji tlk ah tlkahatlkr uskrs erk bs sgedd . Sbjck tlkcaiks mejiwbitl tlk caik sbfjed claskj ta mk gucl derfkr tlej tlk mejiwbitl ah tlk bjhargetbaj-mkerbjf sbfjed, tlk kjcaibjf prackss kjderfks (sprkeis) tlk spkctrug ah tlk sbfjed eji bs tlkrkhark edsa ojawj es sprkeispkctrug gaiudetbaj. Ylk rksudtbjf sbfjed bs edsa ceddki e sprkei-spkctrug sbfjed, eji CIGE bs ahtkj ikjatki es sprkei-spkctrug gudtbpdk ecckss (SSGE).
'khbjbtbaj ah crass(carrkdetbaj hujctbaj>
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
]xy (o ) 7 dbg
J ↝√
5
J ∝5
∕x y J j
j 7>
j ∝o
355
62
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!arrkdetbaj • • • • • • • •
Kecl uskr bj e CIGE systkg usks e ibhhkrkjt caik ta gaiudetk tlkbr sbfjed. Claasbjf tlk caiks uski ta gaiudetk tlk sbfjed bs vkry bgpartejt bj tlk pkrhargejck ah CIGE systkgs. Ylk mkst pkrhargejck wbdd accur wlkj tlkrk bs faai skperetbaj mktwkkj tlk sbfjed ah e iksbrki uskr eji tlk sbfjeds ah atlkr uskrs. Ylk skperetbaj ah tlk sbfjeds bs geik my carrkdetbjf tlk rkckbvki sbfjed wbtl tlk daceddy fkjkretki caik ah tlk iksbrki uskr. Bh tlk sbfjed getclks tlk iksbrki uskr's caik tlkj tlk veduk ah carrkdetbaj hujctbaj wbdd mk lbfl eji tlk systkg cej kxtrect tlet sbfjed. Bh tlk iksbrki uskr's caik les jatlbjf bj caggaj wbtl tlk sbfjed tlk carrkdetbaj slaudi mk es cdask ta zkra es passbmdk (tlus kdbgbjetbjf tlk sbfjed). Bh tlk caik bs carrkdetki wbtl tlk sbfjed et ejy tbgk ahhskt atlkr tlej zkra, tlk carrkdetbaj slaudi mk es cdask ta zkra es passbmdk. Ylbs bs uski ta rk`kct gudtb-petl bjtkrhkrkjck (apkretbaj bs rkhkrrki ta es euta-carrkdetbaj). 35=
*yjclrajaus !'G" • •
•
• •
Bj fkjkred, CIGE mkdajfs ta twa mesbc cetkfarbks0 syjclrajaus (artlafajed caiks) eji esyjclrajaus (pskuiarejiag caiks). Syjclrajaus CIGE kxpdabts getlkgetbced prapkrtbks ah artlafajedbty mktwkkj vkctars rkprkskjtbjf tlk iete strbjfs. – Har kxegpdk, mbjery strbjf "5>55" bs rkprkskjtki my tlk vkctar (5, >, 5, 5). Xkctars cej mk gudtbpdbki my teobjf tlkbr iat praiuct, my suggbjf tlk praiucts ah tlkbr rkspkctbvk cagpajkjts. – Kxegpdk0 bh u7(e,m) eji v7(c,i), tlk iat praiuct u⋋v 7 e*c + m*i. Bh tlk iat praiuct bs zkra, tlk twa vkctars erk sebi ta mk artlafajed ta kecl atlkr Bh vkctars e eji m erk artlafajed, tlkj
353
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*yjclrajaus !'G" • Kecl uskr bj syjclrajaus CIGE usks e caik artlafajed ta tlk atlkr uskrs' caiks ta gaiudetk tlkbr sbfjed. • Artlafajed caiks levk e crass-carrkdetbaj kqued ta zkra? bj atlkr waris, tlky ia jat bjtkrhkrk wbtl kecl atlkr. – K.f. 89 mbt Vedsl caiks erk uski ta kjcaik tlk sbfjed ta skperetk ibhhkrkjt uskrs. – Sbjck kecl ah tlk 89 Vedsl caiks erk artlafajed ta ajk ejatlkr, tlk sbfjeds erk clejjkdbzki bjta 89 artlafajed sbfjeds. 359
"syjclrajaus !'G" • • • • • •
Sbjck bt bs jat getlkgetbceddy passbmdk ta crketk skqukjcks tlet erk artlafajed har ermbtrerbdy rejiag stertbjf pabjts, ujbquk pskuia-rejiag ar pskuia-jabsk (^J) skqukjcks erk uski bj Esyjclrajaus CIGE systkgs. E ^J caik bs e mbjery skqukjck tlet eppkers rejiag mut cej mk rkpraiucki bj e iktkrgbjbstbc gejjkr my bjtkjiki rkckbvkrs. Ylksk ^J caiks erk uski ta kjcaik eji ikcaik e uskr's sbfjed bj Esyjclrajaus CIGE bj tlk segk gejjkr es tlk artlafajed caiks bj syjclrajaus CIGE. Ylksk ^J skqukjcks erk stetbstbceddy ujcarrkdetki, eji tlk sug ah e derfk jugmkr ah ^J skqukjcks rksudts bj Gudtbpdk Ecckss Bjtkrhkrkjck (GEB) tlet bs eppraxbgetki my e Feussbej jabsk prackss. Bh edd ah tlk uskrs erk rkckbvki wbtl tlk segk pawkr dkvkd, tlkj tlk verbejck (tlk jabsk pawkr) ah tlk GEB bjcrkesks bj ibrkct prapartbaj ta tlk jugmkr ah uskrs. Bj atlkr waris, ujdbok syjclrajaus CIGE, tlk sbfjeds ah atlkr uskrs wbdd eppker es jabsk ta tlk sbfjed ah bjtkrkst eji bjtkrhkrk sdbfltdy wbtl tlk iksbrki sbfjed bj prapartbaj ta jugmkr ah uskrs. 35;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
Kxcdusbvk-A]
33=
'brkct *k)ukjck *prkei *pkctrug ,'***•
\A] ah tlk sbfjed wbtl pskuia-rejiag jugmkr ( clbppbjf skqukjck)
•
Eivejtefks
– gejy clbps pkr mbt (k .f., 5= +bt pkrbai tc> clbp pkrbai
2>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*prkei spkctrug ( 'brkct *k)ukjck ,'*-
339
'brkct *k)ukjck *prkei *pkctrug ,'***sprkei spkctrug sbfjed
uskr iete F clbppbjf sk)ukjck
gaiudetar
trejsgbt sbfjed
reiba cerrbkr trejsgbttkr
carrkdetar rkckbvki sbfjed
ikgaiudetar
reiba cerrbkr
dawpess hbdtkrki sbfjed
praiucts F
segpdki sugs
bjtkfretar
iete
ikcbsbaj
clbppbjf sk)ukjck rkckbvkr
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
25
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'*** systkg L Gudtbpdy .%*O sbfjed# s ,t- 8 E i,t- cas,Mώ h ti
c
+y c,t- ?=# (= ta fkt s,t-
8 E i,t-c,t- cas,Mώ hct8 egpdbtuik ah sbfjed hc 8 cerrbkr hrk)ukjcy i,t- 8 ?=# (= E
L "t rkckbvkr# bjcagbjf sbfjed gudtbpdbki +y c,tL *bjck# c,t- c,t- 7 =# bjcagbjf sbfjed bs rkcavkrki 338
'brkct(*k)ukjck Gudtbpdk "cckss • Ibrkct Skqukjck – CIGE ’ Bj IS-CIGE tlk gaiudetki bjhargetbaj-mkerbjf sbfjed (tlk iete sbfjed) bs ibrkctdy gaiudetki my e ibfbted (ibscrktk-tbgk, ibscrktk-veduki) caik sbfjed. • Ylk iete sbfjed cej mk kbtlkr ejedaf ar ibfbted? bj gast cesks bt bs ibfbted. • Bj tlk cesk ah e ibfbted sbfjed tlk iete gaiudetbaj bs ahtkj agbttki eji tlk iete sbfjed bs ibrkctdy gudtbpdbki my tlk caik sbfjed eji tlk rksudtbjf sbfjed gaiudetks tlk
]H cerrbkr.
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
336
2=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'***(!'G"
33<
*prkeibjf eji 'k(sprkeibjf '*** OLz 5>mejiwbitl
clbp retk (MV)
>
hc Yrejsgbssbaj
Meskmeji Bjhargetbaj Mbts
Caibjf eji Bjtkrdkevbjf
2,8 omps
52,= omps -553 iMg (5,=3 GLz)
Vedsl Caik Sprkei clbp retk Spurbaus Sbfjeds
hc YlkrgedJ absk
hc KxtkrjedB jtkrhkrkjck
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
clbp retk (MV)
OLz 5>mejiwbitl
hc
>
]kckptbaj
Vedsl Caik Carrkdetar
Ikbjtkrdkevbjf eji Ikcaibjf
clbp retk
52,=omps
clbp retk (MV)
hc Bjtkrhkrkjck hrag atlkr ckdds wbtlbj tlk systkg
Meskmeji Bjhargetbaj Mbts 2,8omps
clbp retk (MV)
hc Bjtkrhkrkjck hrag uskrs wbtlbj tlk segk ckdd
332
23
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!'G" ]kckbvkr har [skr 5 g5(t)+
Yrejsgbttkr har [skr 5 g5(t) g5(t)c5(t)
Vbrkdkss Clejjkd
g=(t)c5(t)c=(t)
YSygmad
g5(t)+k5(t)
g‒5(t)
∯ >
g5(t)c5(t)+ g=(t)c=(t)
c5(t)
Yrejsgbttkr har [skr = g=(t) g=(t)c=(t)
c5(t)
]kckbvkr har [skr = g=(t)+ g5(t)c5(t)c=(t)
g=(t)+k=(t) g‒=(t)
YSygmad
∯
c=(t)
>
c=(t)
Bgpartejt Jatk0 Ylk veduk ah kb,t- ikpkjis aj tlk crass carrkdetbaj prapkrtbks
gb,t-> Bjhargetbaj Gkssefk ah skr b cb,t-> *prkeibjf caik ah uskr b kb,t-> Bjtkrhkrkjck skjski et
+ktwkkj c= 6 cM k b,t-83 bh c= 6 cM erk artlafajed
39> rkckbvkriktkctki ah uskr b et rkckbvkr gDb,t-> Gkssefk
*prkeibjf caik prapkrtbks •
Ehtkr tlk sbfjed bs crketki my tlk saurck, tlk sprkeibjf prackss usks e sprkeibjf caik eji sprkeis tlk mejiwbitl.
•
Ylk sprkeibjf caik bs e skrbks ah jugmkrs tlet daao rejiag, mut erk ectueddy e pettkrj.
•
Faai CIGE sprkeibjf caiks slaudi mk clerectkrbzki my rkdetbvkdy daw crass-carrkdetbaj prapkrtbks ta gbjbgbzk gudtbpdk ecckss bjtkrhkrkjck (GEB).
•
Faai CIGE sprkeibjf caiks slaudi mk clerectkrbzki my daw eutacarrkdetbaj prapkrtbks ta gbjbgbzk bjtkr-sygmad bjtkrhkrkjck iuk ta gudtb-petl clejjkds
•
Bikeddy bt bs iksbremdk ta levk matl carrkdetbaj hujctbajs ta eppraecl zkra 395
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
29
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*prkeibjf eji iksprkeibjf
MV7 MS
MV7 FMS
MV7 FMS
MV7 MS
Iete Sygmad
Sygmad Iktkctbaj
Sprkeibjf Caik Sbfjed Sprkeibjf
Bjtkrhkrkjck
Sprkeibjf Caik
Caggujbcetbaj Clejjkd
Sbfjed Ik-sprkeibjf
39=
%9 sk)ukjcks • ^J fkjkretar praiucks pkrbaibc skqukjck tlet eppkers ta mk rejiag • ^J Skqukjcks – Fkjkretki my ej edfarbtlg usbjf bjbtbed skki – Skqukjck bs jat stetbstbceddy rejiag mut wbdd pess gejy tkst ah rejiagjkss – Skqukjcks rkhkrrki ta es pskuiarejiag jugmkrs ar pskuiajabsk skqukjcks – [jdkss edfarbtlg eji skki erk ojawj, tlk skqukjck bs bgprectbced ta prkibct
393
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
2;
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
%skuia(rejiag sk)ukjck • • • •
Cej fkjkretk tlk pskuia-rejiag skqukjck (^J, ^skuia-Jabsk) usbjf slbht rkfbstkrs wbtl hkkimeco. Daw tlk rkfbstkr wbtl bjbtbed stertbjf pabjt. Ylk pereddkd autput ah tlk rkfbstkrs cej mk uski ta skdkct tlk cerrbkr hrkqukjcy bj Hrkqukjcy Lappbjf systkg. Ylk sbjfdk mbt autput ah ajk rkfbstkr cej mk uski ta skdkct tlk pdus/gbjus gudtbpdbkr bj Ibrkct Skqukjck systkg (> mbjery har -5 vadt, 5 mbjery har +5 vadt)
399
Bgpartejt %9 prapkrtbks • ]ejiagjkss – [jbharg ibstrbmutbaj – Bjikpkjikjck – Carrkdetbaj prapkrty • Ylk pkrbaibc eutacarrkdetbaj ah e µ5 g-skqukjck bs
5 5
] (ω ) 7
∝ J
ω 7
>, J, =J, ...
atlkrwbsk
• Vlkrk J7=g-5 bs skqukjck dkjftl ah g-stefk rkfbstkr • Gexbged dkjftl skqukjcks erk jat pkrhkctdy artlafajed • Gexbged dkjftl skqukjcks levk faai euta-carrkdetbaj prapkrtbks
• [jprkibctembdbty
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
39;
28
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
'khbjbtbajs • Carrkdetbaj – Ylk cajckpt ah iktkrgbjbjf law gucl sbgbderbty ar rkskgmdejck ajk skt ah iete les wbtl ejatlkr – ]ejfk mktwkkj –5 eji 5 • 5 Ylk skcaji skqukjck getclks tlk hbrst skqukjck • > Ylkrk bs ja rkdetbaj et edd mktwkkj tlk twa skqukjcks • -5 Ylk twa skqukjcks erk gbrrar bgefks
• Crass carrkdetbaj – Ylk cagperbsaj mktwkkj twa skqukjcks hrag ibhhkrkjt saurcks retlkr tlej e slbhtki capy ah e skqukjck wbtl btskdh 398
Artlafajed caiks • Artlafajed caiks – Edd pebrwbsk crass-carrkdetbajs erk zkra – Hbxki- eji verbemdk-dkjftl caiks uski bj CIGE systkgs – Har CIGE eppdbcetbaj, kecl gambdk uskr usks ajk skqukjck bj tlk skt es e sprkeibjf caik
• ^ravbiks zkra crass-carrkdetbaj egajf edd uskrs • Yypks – Vedsl caiks – Xerbemdk-Dkjftl artlafajed caiks " Vedsl getrb ,prapaski +y @H veduk es -5. • Kecl mbt sdat bs hurtlkr sumibvbiki bjta G gbjb-sdats. • Ylk CIGE caik uski my tlk skjikr cajsbsts ah e skqukjck ah G veduks, cg, g 7 5, . . . ,G, kecl teobjf e +5 ar -5 veduk. 39<
!'G" kegpdk
392
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
2<
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
!'G" kegpdk
3;>
:kcep> !'G" • uski bj skvkred wbrkdkss mraeicest clejjkds (ckdduder, setkddbtk, ktc) stejieris • ujbquk —caik‗ essbfjki ta kecl uskr? b.k., caik skt pertbtbajbjf
• edd uskrs slerk segk hrkqukjcy, mut kecl uskr les awj —clbppbjf‗ skqukjck (b.k., caik) ta kjcaik iete • kjcaiki sbfjed 7 (arbfbjed iete) \ (clbppbjf skqukjck) • ikcaibjf0 bjjkr-praiuct ah kjcaiki sbfjed eji clbppbjf skqukjck • eddaws gudtbpdk uskrs ta —cakxbst‗ eji trejsgbt sbgudtejkausdy wbtl gbjbged bjtkrhkrkjck (bh caiks erk —artlafajed‗)
3;5
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
22
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk> *prkei(*pkctrug $*O ,**$*O• Jargeddy `ust trejsgbt mbjery > wbtl ajk hrkqukjcy, mbjery 5 wbtl ejatlkr hrkqukjcy. • Jaw ehtkr sagk mbts erk skjt, wk lap ta tlk jkxt pebr ah hrkqukjcbks.
3;=
HSO 7 Hrkqukjcy Slbht Okybjf
!ajvkjtbajed $*O HSO tbgk wevkhargs
3;3
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>>
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
$*O wbtl $rk)ukjcy ;appbjf *prkei *pkctrug HSO-HL Ybgk Vevkhargs
3;9
$rk)ukjcy spkctre HSO eji HL∝HSO
3;;
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>5
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
Kegpdk> *prkei(*pkctrug 0%*O • Yrejsgbts pebrs ah mbts usbjf e plesk clejfk. • Cej mk ejy cagmbjetbaj, har kxegpdk – Mbts >>
⇝
wevkharg plesk 9;¾.
– Mbts >5
⇝
wevkharg plesk 53;¾.
– Mbts 5>
⇝
wevkharg plesk ==;¾.
– Mbts 55
⇝
wevkharg plesk 35;¾.
• Vbtlbj kecl mbt pebr (sygmad), tlk hrkqukjcy bs clejfki. – Ylbs bs ceddki e clbp.
U^SO 7 Uueireturk ^lesk Slbht Okybjf
3;8
!ajvkjtbajed 0%*O Ybgk wevkharg U^SO tbgk wevkhargs
3;6
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>=
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
0%*O wbtl 'brkct*k)ukjck *prkei *pkctrug U^SO-ISSS tbgk wevkhargs
3;<
$rk)ukjcy spkctre U^SO-ISSS hrkqukjcy spkctre
3;2
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>3
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
0%*O wbtl $rk)ukjcy ;appbjf *prkei *pkctrug U^SO-HLSS tbgk wevkhargs
38>
$rk)ukjcy spkctre Hrkqukjcy spkctre0 U^SO eji HL∝U^SO
385
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
5>9
Dkcturk jatks
Ykdkcaggujbcetbajs KjfbjkkrbjfB my @argeO koedebjkj
*uggery • Hrkqukjcy Ibvbsbaj Gudtbpdkxbjf (HIG) bs ej bgpartejt tkcljbquk har gexbgbzbjf utbdbzetbaj ah e clejjkd. • Ylkrk erk tlrkk gebj Gudtbpdk Ecckss (GE) tkcljbquks. • Sprkei-Spkctrug (SS) tkcljbquks levk skvkred eivejtefks, kspkcbeddy har gudtbpdk-ecckss eji bjtkrhkrkjck gbtbfetbaj. 38=
Gaiudetbaj,gudtbpdkxbjfejigudtbpdkecckss
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