# Chapter 1 - 1.1 um Chapter 1 Signal Period cask 2 smart I...

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Unformatted text preview: 1.1 um Chapter 1 Signal Period cask!) 2 smart) I q A I cassz :- .3 ‘ (4 r) l n z: — 5‘ 2 2: mm: x) 6 J 5:: 4 505(7— r) : _. 3 snap—i r) «25(3- :) 8 3:: l sm(-__- 1' —; J 2 3r 10 c(Md:- f) T 3 3 ILL—.1— f"- "——__.__ . L}, —..J_.—l- ..I-.._sr'..'_"u , as... -1 ........a .— +— 1.2 =1 =r+e' (13) I0) 5.81 =7. l-l’. if u i:€— ICE) is 1.4, 1-5 (Q) —l’1 a they-q I (d) :0} = Zcxp[—r], 0 S L < I, and 13+ I) = *(r) 'z. Lit-133'):- :LE)‘ £0? gv’ch b - :- mc subsHJ-ui-c 3.: - «t-rT 1Ct+1T) -.- th-i-T') = 1th)- "C' 1th) J~\$3 PﬂioéI-c. (dip! PerJCG’ ZT i? we. swash-Ext: 4:.=-E:+2.T tLt-e-ST) -: 2Lt+z‘r) = ILL-D PgYiaat}. mi”! pew'aq‘ 3! 1L&) Partécin'c. city's Pavia; X3Ct) =_ a):.(t) 4 1: F269 X3 Lt-t—T) : qﬁﬁt-a—T) + EXILE-+1") :: aX.(,t) J. beLLE) _: XaL‘t) S {ﬂ 1.11.1: is, . i. 3 PCT lac: KC (ﬁlm [5-- Periclt‘g, gal-Ha Pc-«ioél g. “Tag-1 K PETEQJI}; (43.1% pc‘r1;3& 3 - "T -u - _ I. [-5- (‘bp ‘11P [.3 gt] L‘s Per'toclic. “3:14, [xvioa .; an d! C113 Ir ’1] f5 Perl'ocﬁc mm: pﬁ’l'oc! 2 . 1111!" x LE) 35 Perl-03w. {DUB period __ C. ‘ a ' ‘r'IaJ'c " H] (C) czphzgh] ‘5 pt! I ‘3' u.) a; ﬁxPE‘thj {s Peﬁcdic. ml“: pea-"cod 2%: 111'“- 271' Subcg 4h: gal—{o cf. +h¢5¢. 4-1pm Pcw'aJs , 5. JE- ' '3 {.5 "DE a TQHona-l “umber, XLO 1'; no? Pew-Walla.- 5 . . (d) cxpfg I} IS not pcnodic, so that x(:) is not periodic. 16 (3)7} =_. Tzzﬁﬁ— 8r "7' exp [Uth = Casi-oi: +J'Sc'qw’t: (Eult‘r's Formula) SEW-5' CDSuaE or“; St‘n wt an: Perlgdlic LDF'Hs Peri“; 177/13 J {-15:47 “Hue.” “near combl'nﬂ pm” is GISO pc‘r-‘odfc. wH—k pew-ac! 171' ﬁg . "'3 Sa‘n cc tLt} f5 PcViédic. 03"“: 13:” Oct TI zLat) = 3L La&+T3 = qu LI; 4- 174)) F3? Eta {1‘} 4-5: 1m: {Jr-Had}; uni»: page-cl T] 11:1ch '1”. 1 1"!“ SimSlarlvj I 2Lt/b) = x Len, 4 T) = Debt U;- J-ET) ) For 2 4-9 L: Pew-Each; (9.144., .IXYioc} one. nccds ‘ "I" = 1;:- F5? 5;“ t T‘ = 117' For 51.11 3—}: I 'T" -.-_ 1r __. TI;- Sr an {:11 TL : 417 = 2-:— 14 ' I T ~ {3) P = Timon E-Tzzsiﬁg 0dr r l T \$0 (2.7: = 1m — :' —cos-—r T+oé4T_T 3 . r - ' 1 2T: 2;: _. hm __ __ _ _ T400 4T 3 7‘cos( 3 0d: -—-—+oo so that x(:) is neither an energy nor a power signal. 1' —4l '2, (b) E: r;n;o '[cxp[ Ii]sm (10d: —: 2 I: = I] cpr—4r][! —cos(22:r)]dr = 7:21“: so that x0) is an Energy signal with P = 0. 5 "the n cant. I T; I r I J. axp(3lrl}d.r = lim I. q. —: l eST—I (c) 12:53—- "22‘ WOO sc that :0) is neither an energy nor a power signal. (0‘) no is periodic with period T = 1215:, so that i: is a power signal with 7 — 5in(2—;r 1)} and is periodic with T = 48 secs. Thus T . I , 251: 7;: -, = — —— — - ""_ “d P 4T J[sm( 24 :) 51:1(24 U} I _,25:: I T I 7. I = 4—7.. J5m‘(—-— 0dr + — T .Zh dmﬂ 24 47' 0 5'” (24 U] (0 P: so that 1“) is a powersignal. . V T I T W I! K084}.le f IKLtHldl: - PT lfoLthl :- J?- a 2?” o _ f25:? sm_ 24 7:: r ' '— d: )sxrjtz4 I) 3 Mm .ﬂ. H 2 0 4 __ .9; u ... hv . 4 x * m. _ , 4 - / 3.... / F u 2}". . 2 2 5 w. 4 \ r < < c a . S S <. .r 2 llﬁllunllllllkllli I. I... 2 4 m; I E. a m 3 2 + _ 2 0 .. Fl. __ m. .1 2 _ u. hu 1 .I] I.“ 3.4 9—45 ._. < I? . .| z. ( <_ S I (a 43.4 9" _ 9.4 156 Olhel’w 1.. .21. .2 + . - p OuquTZIJ Elli-IllIlI-I‘ 0 ) vi.)- __ _ + I 713 x (\ 1 .39134 .3 . _ _ <_ S <_ < < < 923435.} _ _ . otherwisc 2t—2 x(t-2)= 2t—6 0 —6r—6 x(—3: —2) = .6;_ 2 0 lSL<2 251<3 otherwise 2 -l <r\$—— 2 1 -:<rS—— J 3 otherwise ,/_Wj -{ [El-+3 —4£r<—3 x(r+3)= 21+4 —3\$r<;—2 1 0 otherwise 4.5 —2 -I5 —I_ 45 n :5 '3': 4 9 3 —r+3 ——Sr¢—_. 3 t; 4 4 3 o “l-1 “25h:— x(§r+-— = 4 3 ~ 2 otherwise 0 ":3 = u + 3“ Lnt"l) -lu Lt-2_) £2,110 1 143(5) XLLE) = Y Lt) - TLt-i) - u (t-z) 1,10 (r—‘J'Xthh 2. uLt) 4 £51-.) J L. (F) ngt\ r: uCJc)u.{a-t') ’ 03:: X7LE)= uCCDSt) : {‘ Costpo \d L_'.' 1-14- (a ) 0:) 1° (—63 Ha" (a) (A) 2(- Lt) L+ﬁ~ ._..._._...._...__...A_. i Ext—t) +2 ea] 2: CE) é[1C-tj) qua] -Ji [26?) — 1C-b)] -x.(_t) 11 -u (if) L— 2. J - . -.2 -3 (b) LL+a3+LL‘R) = 2L. (:3 CL+23+ C—(L—z)) -_ (L+R.)+ (R-L)=2.R. 12 Pk HG Kit) = uCt) - Laure?) xgce) = *‘(t‘a — Yu—a) - autt-b) X303 —- L [V (Mb) — *(t-i—q) —-rU:-—n) + Y(t-h)] been qu = (ya)- yea) (u um) — u'(t—a)) = :- - L YCf-C) + .lc.Y_(_b"2Q+CJ cQa—c) XcUﬂ: .L. [Ytt+b) -V(e+q)] + uu.) __g____ LYLE-QJ-Y(E-bj b— u. lav—0k 11"?— ciuvajrcon oi— X.C{:)=T _ Av (b) Xzﬁt): x.C3L~) = Agw“ u(3+:) :2“ Tu U) I t!) = A :- 1 F Tina. chiral-«Ln of. }(LCE) 5;: can x3 Lt) = x! (’72) =Ag-t/27a Liz) = Aft/2T uU:) {3(a) =-A I _ ‘t'IZT f ¥3LtJ-_/i_Ac ____,> th—r C. 13 "ﬁne. AM‘QFOO 9‘“ “a. w; th) :- rad: L512.) '10:} = X(_{:) 4. ongtJT/l) 1- 0.2.15th—T} T >72. (A) T :10 30:) =. th); o-stt—5) 4.0-7.5 xLe-Io) T >>:_ Co) T210 l-H (a) P, at) = {m : e->o e TrCcsLa t/L. pal-g 44514. (3.0:) is an arch ngmch-r'c. Funchén Lag-n, Pl (0] = All"! -——-I -'> A5 é-aa e 17— £cr f ¢ 0 5 6-90 ér( egé+ c ) 2.. _ 2. = tn" _ 6—50 ‘5'” (ct/6+ ﬁve) ea" Trick/s: +5475.) - —3-._ 7- [1m 41—. = Um 3° era-‘5“ T(¢qe+ g/e) u ' a0 ' 4+ 0 .m‘ L name at” 6T _[ Cash We) = L" :77.— j Sada (Jr/e.) J-t é—50 _‘o A} [I'm -I—- -J[ '5ch (t'JJEr _ C--?o Tr ﬁlo 4'0 _ 1;.“ 1'; m" (gnaw) )w 6"30 1 :J'am £--‘Do P-Ct) Can be usaci as o. rho-uncmaLCc-J t'=: E. model {or I acme . _._ e) =- Lm ] 25 - 1"“ I W l+ 27b 1 ago _‘0 GL++~E1£L 9—30 --0 e I -I ~ '0 .. inns —" E” (#1174?) I 9—) o e --O '1 Con la: mhéclIcJ as Q. é-eud..Fu¢1rJ-lnn (A) P4 (1:) ; If": I 6—5:» W £l+e1 - "0L"— JinaL [34(5) is an evcn Sqmmaﬁc panel-13:1 “3% 230’) = all}?! i. :55 «2—50 Tel" (of li-I' o P‘ Lt) _._ 1;," .3... 1-0 6—5:: VCR-+91) In? no . . E: a”: ? Lac“: 2 Ann -4, 4 é-Bo -4, “(tan-e") . “I =‘_£qn4_{;1 _-‘-—I.n:+._.-T_r)-=l U— 6. F Tr \ L ‘2— W Ft. Lil") can be. us-ecJ‘cxs a manic! For 45; «RU-q ‘CUT‘ cJ-c'on . 16 a) Fritz); an e axp["élt{j 6-50 not-c, “an”; Ps({:) 13, on gun simmel'vk Punch-on (511%; E—(aJ=J.:m e no ‘2—5: r:- Ur) Cunnni' be usgcl as o modg‘ For- 4:56 cleH-o. {mack-or: . 0:“) Hugh". J— 9"” 6-30 Tr * ﬂak. +54;- ﬁﬁt) -é. dn nan stirnmckie. Furrch mm, {3303) :: Inn 2. SI-r‘ 9'5 _ o 6.5:, T e’f P‘Cb) cqnm+ Ibe “:3 as Q Mac‘s: For ‘H‘N Jena. ﬁungJ-ion - " 2 3 ‘ L20 (a)J(§:;i)5(:~1)dr=§—%=—% °° 2 3 °° 2 3 °° 3 (inU—Uﬂ-jr—im: J(r—l)6(§:—§)dz= I(t—l)§§(r—I)d1—0 (C) J;[CXP(-t+ i) + sin; % 1)]60 - gm = 0- (d) I[6xp(~r + 1) +‘ sin( 3;- :na: - gm: = 3—05 + sin(;:) = c435 - (e) J exp[ —5: +115’(:— m: = 45”) = — 5.?” 17 *4- ;.2: p[)f:~x]=_f Hug: ‘09 150;): 0.; Sﬁx+z) 4-0-5311) +0-25'cx-—I) + o.‘[U{K‘3)'ufx-‘JJ 75(1) “1 m; w 1 I r—m I *3 («3 P [_x&-3]=J ((2)42: = o 1.;- IS 4- 0-2 (RX-13:12: (b) X.’.- ['5'] =f FCx)Jx 3 (0,1;(x+z)§~a-3§(X) - _ 0.2 +0.3+ 6-2. = 6.7 (a) P[xs4']-_J¢1[(X)JX —I0 4. z 0.2_ +0.3 4—0-2 4-0-1} A); 3 :a.1+o.3 L o..z 1- o-I = 0-8 5 (cl) Pfxss] ~_ chx)&x -lo _ 9 6 ': o.z+o-3 4-0-24-D-lfcf,‘ 3 6.2+ e.3 40-2, 4-0-3 _—,I ll 18 l- 12. -U:+') Vﬁt) = C uLE+-n)+.fée-:) (.43 1 . : I _;_1_:L\___, “1.. l0 1 ,5 _ Lt} :- m A F 2.; 002)] = i [exp [- CHO] uCt-H)+S(t-1)J x 19—3 db = (up[-cw)] 50:“) -<-z_P[-(£+U] u (an) + J'Ct—r) ) ﬁlo-3 *(t1-l) ' ~3 3 (SLE'H)*C uCt-H)+§l(£—1)xlo N t (c) {LLU = k f u(’r’)3’r I: = {4] ¢LP[—(T+;)]u(r+i) + SHAH? 0) t 4‘! Fu. (£310 L2.) -I (b 4' {,kLt) 3 l— :1!) [- Cb+l)] N. (3) t): FKLE) -.- I..uP[-a-+.)] +u(e-,) N 19 1-23 (3} 1-1:): 5(1) + 55\$ -1)—- 25": — 2) 360:) I 4 .5 “i I _ _ oT—j J r-.. (b) x’(t) = u(t) - u(r- I) + 260 —2) - x"(I)=5(r)-~5(t— I) +25'(:—2) If (t) a... 20 k-u: (c) From Equation [1.12). we 5:: that :10 = 2a(! + I) — 46(1) - 2:4: — I) ..n d. (I): 26{t+l)—45'(1)—26(:--I) l’t't) 1L 0' ¢ "”" 4 T hxﬂt‘) T .4: 21 ...
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