Exam1SolnSP05 - ECE301 Signals and Systems Q Spring 2005...

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Unformatted text preview: ECE301 Signals and Systems Q Spring 2005 Exam I Solutions Professor. Zoltowski I TA — Aung Kyi San asan@purdue.edu cavern“ 515%.va ovemii sys+em git) = f 4:4! (a) Linear? xlm 4:. 3.9:): If £4; T-J.‘ .- f‘t S-‘E [QX‘C-M+ bxzf'kjjd'hcl‘t 4:.” —.'L ‘ me overall Syd-0m is Linear. ECE301 Signals and Systems Exam I Solutions @ (b) Time,— Envahi cm+? t I mt) ——al 3 |———-> ylt-b) = Q ST x. (Mamd’t -q -1 x2(+)=xl[’c-’cb7———)|E—_> 32m: 3’: 3T “(mdwl’f —l:-l* T—n. : gt ST 31(fi_t°') ol’hd'c 4:__K‘ TL} '3)..." \ {3-450 x I (a ?\ d 0; 41-450 Til. . It ~‘ 7 ‘r. ‘ 7 LANE ft_1x,(md?«d’t 33100 me-MWmfiwn£» (c) Brnpqlse YesPOnSe OF ovarall sys-l-am muaft I]: scan and? t~w T—l = ' i; [met )—u(’r—=z)] ‘aafi-t“ -‘+ ECE301 Signals and Systems Exam I Solutions tgo hitL- Ogigl 2mm 4— gigs 17,4 I hat) (d) cam/30.1.? No+e +hod- ‘Hne overall 5ster is LTI mm; o for t<0_ .’. We LTf overall WW is causal. sf'cdole . m meta: 5 act—k6) I: —oD r—xs x (t) 4r) qk ECE301 Signals and Systems Exam I Solutions 431(3)) 5:: m (h) wC't):tj(3‘U Period a-F butt) : _€1_ = ’2. ¢__ 3 (83 Tim; no.1an Pmperfg) ECE301 Signals and Systems Exam I Solutions ® HHemai‘we SolLd-ions for {Paris (00,00) and (c) of Problemkti. (a) SySl‘eJmfi'. 20¢):ch Xmal'i: 99 {—7. (lo) x,{t)--> it‘“ = It X'VD‘“: +4. xztt) —; 210:) s It “mad”: Jc-a -{:—1 sysbm (1) is linecw alsltrnz: ‘l: “film #9. 33+) = it Hi‘ (TMT. 21%) ——> 91%): It 11(1351’1: {:44 23(t)=q%t(t)+loazct) a 339:): thH[Q%!(T)+‘o azc'cfld'c :Q t %\ 'E-H . Syd—em (2:) 'Is lineav,.4-——- (B) F + SYerem mg; ; x‘ (t) —> at (-12) = LC 2*. (md‘c t L— 50:): x,U:-to)-5 21%): LC 32‘de =f t— eat—to) = L: at: K:C‘t)al‘t = 22H.) a a o (I) is TI.4-—-—© ECE301 Signals and Systems Exam I Solutions 0. SW]ch LTI SYSRyYL Tm overaiL syskm is linear , 2 'HVYli—MVW. (c) impulse response of warm sys4em = convoiLd-im 0+ inch/ide impuflse Yeapme 6? 9min syg-kam 'm Hm, CQSCW COhQLed'iah. S),st 1 2 Sstremz: ‘1: Imam): St Srnol't hitt) =5 5C‘E‘30l’l? £-2 “‘ t o<+gq -|: hi I 0 (42(3). 2% - 0 91.3191ng 0 medal in mm 11.63:) 1 but” hit” 4m 7 o 1 > i; o 4 ‘6' kHz) 2 h(t)gh,(£)*h2(t) = {1:5, *IE'IZ‘H = %£ 4. ECESOI Signals and Systems Exam I Solutions x [h—1]+ K [10'] + th-M] kin-(3+ "2th + Etna-1] zCn—l'J-ri‘tn] +2tn+1j 'x En~13+ xii/wad] at 2(th + xtna'j 4. x0034, xEYH-fli- 1013+ KLn+13 + xfn+ 2] = x En-2]+2 Min—.13 + ’3 xth3+lxtn+fl 1- xth+23 [G7 Knew? "(1‘3"j '9 51E“? ‘ XIV-“43+ ZKIDn-d] + 3x,[n]+ 1x15”+‘3+ "r CW1] Kltvfl e v7,th :: thh-2]+2x1[n~|3 +3xz[yfl + 2x1Eh+ 13 + Mm 7.] X3, ['33 = 9.99130”) + taxi [h] -—> 931%} 2 ax‘En—ij +sztn~fl + quitml] + 1bx1[h_|] + 3‘1 X1 w + 3b xzth] + 2a XIEYHI'] + szz [n+1] + ‘1 xl Eh+lj+ 19x1 [n+1] = q [X‘EhJJA- 7. MEMO-b3 x,tn’]-+ ZxIEhH] + x,[n+ 1]] + b [x2 2x1En-I'J+’3 nth] + 1 x2 r“43+ K1En+2]] : 0. B'Ehjf '0 filth] The owc'r'aM. Syd-em is linear. ECE301 Signals and Systems Exam I Solutions (b) TI? MUG.» filth] 2 x'lZn—l')+1xIEh—I]-+ 3 xltth, 2 xlfh+131~ x1[h+2] K201] : x,Ch-v:03 *3: Bath) 2 Xz-E‘nazj + lxithql'] .f 3xlb‘] + 1 x Itn‘fl] + x1 Eva-t 1] = .1‘ EnhnDJIJ-k 2 x, Ch~h0~l3 + '3, xI [Io—an + 7. x‘ [h—h°+l] + K\ Chant; 2.] Y'Ln’y’o'] -'= in Eh~h0~13+ 1x1 [Imago—1].}. 3x' [hang]... Zx,En-n°+lj + Kl [harm-+2] = with] The sY SM {5 Tim!” ghvmomi. (c) IMPIMSE Res\)onge‘f Min] = Stn-13+ 9.8 [no—Cl + Eé‘nfldr Z6Eh+fl1~ 5004.1] hrhj (0D causal? No’re Jfinall- ‘Hne overall Sysi~em13 LTE ‘ hEh'] ti: 0 {or n (o I .'.The WM 35 133: causal. (a) shalom? no 2: th‘nll = 1+1+3+1+l=q <oo kt—OO Tfie 3y 81mm is s’mlolfi. ECE301 Signals and Systems Exam I Solutions 00 (1°) mutt-=2 55mm] ’1‘“) 2rth Idth = Kfn] 9(- [OED] 12.3 glib] <--> bk “2.4%,«5—4—3 .24 012 3456 73 Let 2 En] = HEnJ—ljtnu'lj ECE301 Signals and Systems Exam I Solutions [4% o,i6,tl1,..- (h) porn] 2 xEnJHXEnmij By Ffrsi‘ Cli'Fer‘ehCQ. propeH-Y I 414;}: c:k = 61K (I-—e e.) : é: “fie—“(5613) +— ‘FOY all k. I4 you vismflize X'Cn}- xtn—l] th']_xEn-l3 01 eggs 4 obvioug Jthak 4k Eu) ée 6 «(m— {-0er- ECE301 Signals and Systems Exam I Solutions ® AHemai—ive SOIL-WW 120‘" POD"*8 (‘1’) U") and (00+ Prom/(Meta, (co 2 SyS‘RMnii Lb) £th L- xEn—JM. xth + xEn+l] K'Eh] .9 2' Ch] 2: NEH-411* XI Ch3+ XI Eh't- l] Km] .9 31m 2 szM'J + xzth3+ X2 EMIJ *ath'l =QK,Eh’}+bx.L[n] F.) 25th]: C: xlEn—I'J + '0 K2 [Vi—IP11“ a [Wild-0 xztrfl +qxltn+d +la xtan] w: q [xlfin'J-i- flight—13+ XIEh-H'J] 4- lo [x1 tn-I'J {- 2(1th + xztmn v = Q2lthj+hizrh3 . . Sys-l~e,m :L is “neat _c__ @ SYSk/VY) 2.: 9E”? '-'- 2 [V1qu + 35th + 25,443 awn-J -—a 9,003 = 2,5347 + 2.[n3+%\[" + *3 31th a 151th c azfinafl + 551th + %7L“+‘] UV] + 3500] : qiitvfl +bELCh-J 653:”): Qifln-IFJ + 192100 ~13 1- evil ' loam-+4 mmlhbafim‘] 1‘ <1 filth-.1] 4- iflnM-ifi“ “111‘ 5&2?” Elihu + aanH-J] = a 311W) #bLj—LEWJ 2 is “near 4— ® Syfikjm i .' 7:,th -——) 315w]: xflndl-l -+ x| -:. filth—n + K—an'J-r main-H] '3 KI Ch“'% '4] + 11C“ ~h°-.] + 1' th—hb-{IIJ E1130 mo] 2 XICnmon [—1 + MUn~VJ°j + x,th_m+q 2 ath [n3 + x, Em- I] KLth'] = x,£n 41;] -—3 "$15,103 ECE301 Signals and Systems Exam I Solutions @ Sigh/mi is T1. <_____ © ago/n '2‘. I a in] —% thU = $0011] + 2151] 1- itfn-t-l] *3 91h” = 552.1“43 T filth] +3~Llh+13 = ~21 130410-13 +%,Th~n°]+%.YIq—nu+fl 'Hflhhnoj 2-. filth—V10 —1] +42, Evy—ho”) 14 2-, [h-ho'b l] = BLDG {filth} :: 2‘ [Rn—100') .2 813+?!” 2 is <—e-' Ram ®2© Cc) 'trnpudse, scanvduh'm of. h avg-[em 1y, 'HM, Conn-cdfi'cm. gyekmCi) mm = 8 Em] +SM+ HMO ‘ htthl ...
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This note was uploaded on 02/19/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue University-West Lafayette.

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Exam1SolnSP05 - ECE301 Signals and Systems Q Spring 2005...

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