Chapter 13

# Chapter 13 - CHAPTER 13/3.I.£0~>:ZL‘nJ-={3131 2mm =...

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Unformatted text preview: CHAPTER 13 /3.I.£0~> :ZL‘nJ-=' {3131] 2mm] = 0.21:, In] + 1.? urn] lath] =xrn] (b) PW n Mi”: Mi: ﬁrm-2.3+ 0.95171] =' :4 En] III“: '7 I, fn+l1= gfn+11=zztn3 j X; [n+i]=5fn+lj = ~03 3En3+utnj=*d.\$’z,fn3 “‘53 2.1mm {:9 \$125M] +[ﬂurn] 14m: 1:1 6131713 Lang}; W m3: ﬁrm: swarm-awn] 5En3= 11%] 13.2. to.) she) = (1-8) he) +0: 3X11!) we) -= 43‘ Xde) =7.) 4’11?) .35.... Yb?) 2? -u-oc) 141-4)?! 11En+11= a-agx,rn] +4 M.th 5En1= 1.134% = mama] Mum-J Lb) a.) w, W all) 221,122): mama) +0! Uta) «331(2) 3%)!)(2) _ dues) . We): (wax, (a) +4 052)— a- U10 +4] Um») 5.3. m 1L,tn+11 = (1-4)’1£,rn] 4- L 1-4)Tgrnj—+4 um ' ' 222m 0 =zzm1 + \$13, an - Tram] + \$- and 3‘ In]: 3 [h] = LEM-1] --— (1-4112, In] 4- U-AT'ZZL’YI] +dMD1] 52m: 4,-9.3.- yarn-H] ##3th +u- 3115an é. um . _ 1-K H 4 ' ' 3' In“: ' [-1311 yak M *[9/11“ m .=- [-4 1—4 x urn-1 gm [1% we gm] {é Lb) Mama-ab, 4a. Yarn-HI a gym) 2'2 I'm-1:0 Thin-H] = 0-01.13] +4 urn] ﬁlm] = (.I-allfﬁnj! +4u12n] /5. ‘5‘. (a) SEHHJ- 0.95Dﬂ =A5ufn+ﬂ am) a . ﬁnwﬁa 312:1: ‘3 1:113 Lb) yrnHJ roﬂzrrnj +£41.11: gin]: /. 521714.51] :13! 7.’ E 1134-13“an (d) A=I0.9];B=[1];C’=[1.35];D=l-5; In, d12552tf (A,B, c, D) 3m] (6310-) 5933.5: 0 1 0 ' (b) 1 Ina-11:. J's-lath] +[11LLDﬂJ- 5 Eyﬂ: f; a] _ Z 03“ Hm ' £’--L5i'+&3 PE) {4.) Farm 2'. ﬂ 0 I 0 o Cbﬂl’nﬂk 0 0 1 _ +0 urn] 6.72 -3.‘i 2. 1 [ﬁrm] = E2. 6 013131] [3.14. La) Hm: -—-——-——-£-—-—' 55—2.?a‘4u3ﬂt \$.72 13.5. (a) “W 7 o (5) ﬁrm: 1] = 0.8 XIn‘J-I-urnj 5M=-0ﬂztn1 +14 urn] (c) 51313—- 0.931314] 1- 4urn3—3.6uEn-ﬂ (d) n=[4 -3.61.- d=El 43-8]; [A,B,C,D]=tf253(n,d} (e) (a) 525%: lb) 0 1 o grumpy mJXEnM [1]“th [in] = 2. '1'1 [n+1] +32, D1] = [H 3.92]g£n1+ mm] (a) gnaw-1— 1.94 gfh+i1+035fﬂj = 2u[n+z] + 3 £431] (cl) . . - I o 7/227, 73.5141) La) gfn+33+235rh+21 92:1 arm-1] “3.453511 (can?) = akin-+2] - 3.} “UH-j .5- 1.7314131? I ’zls Z" ‘50]! I (d)MI¥TLAB. ztnm:[ I o o 1:1”ijka o 1 C5 C5 gfh1= [2 -3.1 1.73] 513:“de m as £4), win Z,MZ3MM n=[2 -1.96]; d=[1 -.993; [a,b,c,d]=thSs(n,d) pause n=[2 o 3]; d=[1 -1.95 .8]; [a,b,c,d]=tf255{n,d) pause n=[0 2 —3.1 1.73]; d=[1 2.3 —2.1 .55}; [a,b,c,d3=tf255(n,d) 13.5 .m 16.5mm =03 mm + utnj ﬁlth-H] = [.4]: 21:.rn+a+2.zz.m 1- 03%;“; =1. 41.7.1, 3:, In] +2uIn] + 2.2x,rn3 + a? :22 In] =5.” 2,511+ oﬂxzrn] +3.2 urn] 11912131] 9.? o 1 -. grn+a= ﬂ D'szaulmjum 13131]:- [o 1.9]; [n] (b) _ - = 5-5-9 0 ] ;;zI—Hl=(a—a.9)(2—oﬂ)=Aca) “I m [1.08 z-M - 2-0.? 0 I Hi2): CRI‘HI’EZYE'IO l'qll'éﬂg 3-42][3.Z] _..l. . ' — .ébfgﬁitALéj .Ampm‘ 132 15211.32] -— lzw'gxamﬂ) (c) A=[0-8 0:6.08 0.9];B\$[1;3.2];C=[0 1.9];D=0; [n,d]=ssth(A,B,C,D), pause A=[O 1;-0.72 1-7] ;B=E0;l] ;C=[6‘69 6.08] ;D=O; [n.d]:ssth(A,B,C,D) 3171:]: [5.43 4.133] ZIn] - g 2' “I - ,, a 2:- ; 0, 2.: . m an} [m “7] J :21 m 2 172+ 7 Ale) -1 I -' . Hie):- C ['zI-HJ 5 ‘13-” "Daimlig _ J— 1 _, 4.0924'6J? ., “ARIEL” ﬂab] " Ez-IJE +0.72 £33 588 (c) _ 0.2 1.5 1 ' l3. 7, (A) gin-H] - 2.3 0.7]an] +1414!“ 3fn1= 17.7 M13131] [1,) 21:. g: 2-0.2 -/.5 JJ 12I'913Até) = EéA-é—i'l'aﬁé '33; “2'3 5‘47 =21 1.52; —z.?? H:2)= c tel-5'le = W “his 2,553.2] -_--—L W M, 2+23 _ 4. a 5.5 Ah!) '7 22w, " E die-2.3? £03 A=[0.8 1.5;2.3 0.7};B=[1;2].—c=[1.7 1.6] ,-D=O,- [n.d] =ssth (A,B,C,D) , pause A=[0 1;2.89 1-5] ;B=[O;l] ;C=[5.03 4.90] ;D=O;' [n,d] =ssth (A, B, C, D) 3.7. ) .. m- - (Lodge gm“).- 23? 1.%]an]+[?]urn] 3541:1303 4.9a]! in] [-9) 5:: (a) I. 2'- 1 H63): cceI—A)"B+D=D.5 4312"]: O-EJFJ +1 “I H 95 = I ._ .L a 1:15 1314 .?5é_1_305]+2= I.ZB§£+3.§9££+2 z Fonz-w: = 23 - 5.03:2 +5.05% 2?" "/32- +0.2 (e) 2; [M1] = [:2 1;];th + [ﬂan] Hm]: [5.0345—141xlrn] + [-5.035 +3.L]-x,,rn] Hutu-l = rams -l.95’5] 1.6sz +2 am] an (er-A1: L2 —1 1,, laI-R\=A= 22-132 +0.9 .2 2-H '. I o Hts): c Lax-3r ‘3: [3.9245 4-43 533'- [3’3" ,3”, J *2 .. gal-5.055% «t— 5......50-9é z _ l J, -I. 3.4m! _ [33mg “Baddn gElﬂz‘Mj *2 ant—1.994153 at n 3.2 a E a h] .33 , , 3.2 m me): Cal—AVIS =- Ll-)("'""2-A.22 ‘5'” ‘5 -Ma (AMA) 2% ._______.___7asrﬁ_.,_________*w l3. 3. (d) a an] (e) Z Fn+l1=ﬁugllrﬂﬂ +krn] Law?) [a - grin]: 3.227111] ﬂ 3'2 3.2 (9) HQ) g agar—B)" 3 =£3.z)l£-A.22T'm = 2,6,3; {Maud- co¥car—m=[: .' ,5] o ' z?- . , -1 = j ; ; 2.1. “Hawaii- A) B Obi-IL I 241.2% = :5 I FEE] = Ji— (53 Fun. If; and 333% z“) a - ——9 mam-F 5' ?]?L“3+[0]Hﬂ - I355 1 a I - ‘ 3rn1= [o z oi!sz- HL23=E0 2. MALE 1.1][3140 2o] \$1]? 2325,. 2’- ' " MATLAB: a=[1.9 0.8;-1 O]; b=[0; .95]; c=[1.5 —1.3]; d=2; [n.d]=ssztf(a,b,c,d) a=t.821.- b=[3.23; c={13; [n,d]=552tf(a,b,c,0) 5.2 [.7 "' (h) = 152-13 Hpm £‘-/.72+A! - 6‘4) 31:114-le - 1.7 51:11 44'] +0.2 gin] =/.5'm In+l]-/.3mrn'] ml) warm-13 = 0.99 gm: +etn‘1 J- mm: =2x3rn] [3.9. (at) 3131-1-13 = L0 I 12 In] +[ﬂmrnlj gumsf-LB [.512]:er Le) new) £9) MON-£1 —o.42mrn1 =3 e. In? ‘3’ [‘33 II? 2 ]zr 34:3} = " n I a ’1 3mm 1.3 4.5 0.92 I “"1 gtn1'=[-.3 \$5 9.114th 2%: —u—.-_.-._......._.r_‘.. .- l3ﬁi11.) (ﬁr-A) = jg 2.3.7 '02 ] -1‘5 [‘5' f’b»73 Jar-A I =4 = 25-2. Liza-H.151. z --2.1 — [-35 -o.32- 443.748] = 55-24: 22+ saws—3. 524 i 9 ! l Car-A) = . ' :I , . 0 I-Im-—C£zI-m"3=~1}1.3 £5 61\$]: . . 222': Mo] . , aim»: I gal-[~13 1.5 a} a]: 32-2.; £3 (11) a=[o 1 o;-o.8 1.7 2,-1.3 —1.5 .98}; b==[0; o,- 1}; c=[-l.3 1.5 0]; [n,d]=ssztf{a,b,c,0) (j) H xi = (gal—M, 315,3): 52-2.; ' 23-2.m’-+5me ~35” i i +£‘)C') _—_‘_"——_——_ Lb) I; Inrsz- 2.423 :sz +5.14: 3 mm 633933“ =-' 3nIn+\1—2.é nth] Imam) Fm mm. 13.2: 1,rn+‘1=u-4)z.m]+x urn] 3m -- z I-d)1,tu]+4 min] 1 Ha) Ha) = CLEI‘BTIB+ D a “"0.-3-a-»:)"z +4 = «cl-ac) Mae-(cm) = 4 2 5 ~01) .2123. fin-£4) From FM!» 133: _ 1—4 M 4 ] ZInJ-IZ—Lé/T l_ﬁ]zln]+ an urn] Jain} [1-4 :11] gm] +oc utn] up) z—r-A = z-u-x) sag) B/T a—a— 1¢3p=o)ma)=_a-aoreoc-4‘I ﬁgm 4+ 5‘ a (1- (1-4) ﬁzz-4)? +010 = 3M1).- ., 5 2- ce-nla-mo) a-u-x) K372 261 .. 0.2 1 an.me 0.?]grn]+[3'z]um 5TH1=E¢> Hutu] l3. [2. Ca.) Fran Rib. Bialéd: Lb) Frau Pro is Laban): i " Ola —-———-——. l :3 (21- HJ'l-g [ii-b.5062 ma) 2-5? a C) :57 "é-y =2 w M .J—u— (4m -a. -o. "Jae—MHZ; a] L-a!+é-ﬁ.7 e-o. , 0.? “ o ‘5. ’dig‘] a. _ H in) 1cm .2 I.’ 7: = [’]=[ a? - 1 9 "J- D: QM z 432(0.9)"-40.9(é.3)" afﬁl'l'ﬁzrv-PWW n20 (d)_)_(£23=(EI-R)"BU&)=I 3%,"; o H: )2 2 j ._.— He-mszz-am 21517 3. 2-: 1 . (2-: a-a ‘3 M 2.33? f ca-amtz-aﬁjza-i) 51“!)(2-493) :15. I: 55' +23%? ] 3 :49! .53 “3-3 gr £3? a-nnfa-I * a" g [ z - 503.9)" ] 5-3 6 4- 30% no.9)” 14016.9)" Ce) From Prob 13.6, Hag): Ci‘ “6-9)(2 ~44) YE) [#22 042) A622- 69 632{ 5 /2// ._-—o = ' -- , a .2 5 a '3 ‘9‘133'0-912-533 ' z}— +£3.72 the}? 5m =- 43“ + 572 7w.9)”— 121\$..2wﬂ)" (5’) 51m] = é5’2.5+ 452.240.9j'1-M9A9Ka. 9)" grnTI=D-7 14] gm] 23.13.14); n+1 -.— 0.2 o : z 1 o o. gmnyum J (b) air—9:??? £33] J- laI-ms- ca-o.3)¢2-—o.1)=A o _ , _ -'.- .2. @m- scar-93’ -3- E39"? 133,3] {3—49 a- ” 3-0.7 “2%8 - ,—..-—...—._‘....‘_ b) in“ ‘5 Tim] 313531103“ gn In] [I 'I 11.le _ _ _._. a. = * ‘ - (C) 3 [’1] ‘ é 5"] XIDJ'E L LO.an 3 ,3 1,759.9)"4-3 .2403)“ '2' 0 E'ba = [s-Dle-om] =[_gﬁ. + £352; > rm au—asn) ] J___. - '0: :- __ 2 n h ég-Lli 4., -é.1,z& 5'7 ) 34M%¢L7 gm] =c grnj= [1.7 1.4,] 1:. ] =26'0-03")+m.ua-a.7)“ _L* le)HLz‘:)=Ct2I-Q)"B=Du? 1.4] {ED-,3 ﬂ 1mm; 1,1,] 3-49 0 2%? 2' "La -9".1 . ,, 1.1 3.2 "Hm 02 {iii}: :2 Si? 2,53 10 L12- » m 73" Hm”) Mia-ofé-Tﬁ-ng a; \$13.? " all ‘ 3.33" grnlr- 3-50 -0.2”)+m.b7a-a.7)" n n w) 373"] = /'7lb-Q)”+3-2w,7)"+2.5~2,516.2} +Ia.g7—M.5?ca.7) w. 17 1.2” .91"- 7.9 714.7)" (33 51:5} 11.3", 3152]: 1/.1'52 " X1(‘1}=1; x2(1)=2; for n=1:4 Y(n}=1.7*x1(n) + 1.6*x2(n); x1,(n+1)=.8*x1 (n)+0*x2 (1134-1; X2'(n+1)=‘0*x1(n)+. 7*x2 (11) +2; end Y - r- = a - - 2 - ‘4: -'— 4: 13.14uaglf- A a z1],}!2I mama) [g it“? "Hater-m4 = -I I J. _ 5m Stu-I] 5 13!:0 liq—[o 5th t2) 931:)th 5”): IE ?1 J Q111=A =12; A] W Az-‘fz All: AP [3 2] n a z , émr- gm gym] :3 <3] .zgmism Stu-1]] o 5 In] 211'“) > In] ' .- mﬂg ..RmbggéﬁlimmmMolahg‘, _ z -1- A o 23.2mm zr-n= e 0],!2I-AI-E , car—A) ﬁﬂé "W791 ‘ 2 o .191h13‘[2[£]:'g) ' :3 [Be '0]:- sin] wwwAﬁéw-“B‘ﬂ a 95m=A= 12 f’ :1 @W 62 mm o "zééW—Q ' a — Sin] 0 "Q m ’ [sun-:3 5m 0* m mar-- E? 213%] £DI= 19,313]: egg] 1’]:ng , 4,313.1:9) n3 2_- - n1 (0 Hm] z ém g ["1 =[233n 5%1][é]= [22:13 +5 ran-ﬂ] ﬁrﬂ" ’50 13.17%] = 25131“ Sin-ﬂ {6) gm: c ZZoJ=Q I .25. DJ“ 92:10} +Bum] = [{]u!=[}]5 3EIJ=ZLUJ~_ zm’ B {JUL}: {10" ,‘gm izzwzé. 1£31=[?2][2'_]*[f]¢0=[£] J 53322. If”??? SJZiJaLmu): [,1] J‘HI‘lJ-‘é’: OJ H30 .'. 3th] 3"[1 Jypl Z J naz 1 l. I ,1. - — = - .. e g -.- '1'! (-91) 91:2) =caI are We) jugg- [, 15., Lang; - . . I Yea) = eggs-yrs: 1') D] = 57157,) +27,- .'.5rn3= 3" Ym = urn-z - cg} Hta)=CzeI-H)"B = [a ﬂEi 2'3- QI .'.Ym= H£2)UC§)=[—éi+ 3th]: urn-z] +urn-x " (b) x1(1)=o; x2(1)=0; for n=1:4 y(n)=o*x1(n) + 1*x2m); X1(n+1)=0*x1 (n)+0*x2 (n) +1 ,- xz (n+1)=1*31(n)+0*x2{n) +1; and Y _ h I Jazz. (4.) gm: 3 (gI-Hflza 5.757;; = 23.95 =7érnJ—035 (b) mm = 15921 1: tor"- 035351311; sz: 3:035)" ‘2420 I3.» cc.) rzmoﬂi 21:63:03: 7 11-53";- 0.?52'[21=(A.?5)5 (“W 21:21: oﬁivzmdatmz m]: (5.95)" (d) xm = (al—HJ'EUB) =2cj§50)(§%) £2)- _ _..l - 20 -20 u % “dz-xyg.¢,m " §:—+5.0_95 => 21.72:! non-M; )Jngo gird-'31 rnJ=40{/— 0.95”)J n 30 ( ) H12) CLzI 5r3-£_m5 WE)- ___~i____ .. w - a '3" le-1)(2-o.95)' 27-7 “‘4'” => 51”“3’40U‘ 09-5.”), '36 iFoxkf l—F) u=1;x(1)=o,- for n=1:5 Y=3*x(n) x{n+1)=0-95*x(n)+u; end [3.17.650 Fram Prob 13.11,) H15): in; = 3%: w P1“: :1) ram 1] ""' Au; PjAP= [31 1‘11? €1L’ﬂ-{f 1 [3’ ﬂat: 3'} B«=”'5=£-f I’JI:J=L;] Cuv=CP= I0 1383:“ z] '. {I'm-H]: I‘: ’1'1m-I-[ﬂum ,‘ gEnI-VII 2.19%] (d) Eur-AV: iii-Ii ll]j[&I—AI=32=A - it! Marga-APT?” =13 25' r [I at? "3:! m z.=2,.=o ’3‘ “— (13.1.7) I'z‘I-A|=2"= [fl-Ar] = ce—axa-o) 03.1.2) do! A=o =dut A V: (0)60) £13.“) Ala-=0 4&4”. —- Mo ac. )Le.) a=§0 0:1 0]; b=[l;1]; c=[0 1]; d=0; q=[2 -1;—1 1]; P=1nv{q) ; av=q*a*p bv=q*b cv=c*p pause [n.d1]=ssztf(av,bv,cv,d) ZZH 294.031.5245.”:55 P . . = [3.3.0.11 Fm '3{” [38/ Ha”) 51-1,?5+0.-3 m m :1; Fiﬁ. 11 MM F ii 1‘][if‘ °§}[f ﬂ ’ 3% -.'5.‘9][i L] = \$77-55] Bar: FAB: j —Ii}[£ﬁ5] 3 '3'355] c9 = c P 47.5 4331:: 2:14:33 4.11,“ D,» = 0:3 "- ﬁfth-HP 4!sz + [fillim 3:111:1392 '1-1142'131] +2 (d) EI-Alrf- 2;? 5f“ JIeI-A|=aZ-1.‘}2 +0.? . _ - , ~53; manager-AN.) ‘B,+D¢=[0-Z 4.1]: :25 aiﬂ][a.q5 *2- = ﬁll-231F437 -1.Ia+szm = W ' a. l = (3.2.2) Ad \$0.2 = dd: ﬁr= (1.27)w.z.s) c 3.44) a )9: 1.? =25» 9,,»- Layaéa (cues a=g1.9 .3;—1 0]; b=[0;.95]; c=[1.5 -1.33; d=2; q=[2 —1;-1 1],- p=mV(q); av=q*a*p bv=q*b cv=c*p pause [n,d1]=ssztf(av,bv,cv,d) Jan, to.) Hum Pmb. 13.13, 0.5.: 511.7?+0.2=(§-Ag-7)[£-d.&3]=o MM (b) m: Lung £25.43)” (a) a=[1.9 0.8;-—1 O]; eig(a) a=fo 0;{) O 1;1 o l]; eig(a) Hm MATLA 8,. a: 1.41.54, 0.234 [2104.46 .’. W n n . )n (b) m: unnan , Eugenia. 7724)) maszsvum ...—.—_—._.—___.——____ 2.42 ...
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Chapter 13 - CHAPTER 13/3.I.£0~>:ZL‘nJ-={3131 2mm =...

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