HW11f08solutions - EOE 201$.“l Fall '08 ' Purl; SoluHons...

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Unformatted text preview: EOE 201$.“l Fall '08 ' Purl; SoluHons ll.l utt-s) nit-5') utt-fi-uLt-S') (A) \I '1 I: I 0 73 -t 0 5+- 351: Mt ~3)-uc5»t) “Lt—3.) “(S-t3 (b) . o 3 I :t -5 O 5 t 5 s t 90m 9919' XC£)*SLt'EJ) #687”) (a!) cost-t) (sctnr) —S(+ ~11)) = CoSC-rfi 'SCtmr) -Cos (flat—1r) = — Stu-n) + €Ct'fl) (e) f“ (pact)- Cs (vrr) —Sc‘t”rr) ) at = j i'iscrmrwt + J” guru)“ 2—1+1=o n .l (conlru) .p 't () J CosC’t)(SCT.1-'fl') *SCT-W‘Dd’t = 99 4: “t _j Sf’tflrfid’c + f SCI-4100‘ '5 - 0:, 90 ‘L \L _ -1 t 2 -1r _ I t i’l‘r { O t < —'n' i o t < n- (Thc. Problem da'dn‘i- ask. For a fi>l9+JbuV “‘5 had—19%|) Plotting these'. o dsewhue u. I (con+'cl) (9) (h) “£6” SI'HCZ'L) UL’L)SC't—l)dt = I Shah.) 3071—0617: =SI’nC2.) --09 (i) If. SMCZ'TZ) aft) SCt‘T)ol’C 5; (think. 070 1: like a wns+m+) L . on f gm (21:)- 5’ (Lt-'11) d? = 3m £21)- (A He) w . “———II—I—II- (J) 3— (ezt Hue—3)) =eltiuLt*3) + MUTE) 9L2,ch = t“ 0H’ 0H 32+ [Sat-3) 4— law-3)] 11.1 (a) x(4-,)= uLt-I) X(’t)=ul’t-l) ut’t-O l "L'. -(z~‘t) _ -t ‘9 uca—t) (5) Mt)“: uLt) i=2 -671) 1. h['l;"T.) = e. (AC-kw) .w-ww/:/[ .2-m mmmmm ._. "L {2’10 ('3 Mara-Mt) hClO‘T).IxC‘t) % k c} :2. "C t lo Recall 3(2) = 501(1)- MZ-“CM 't 500) =5 93(1) hLl0“"C)d'-C 09 O0 — ’ It‘djmfi 53 the arr-ea; 010 again: I3 (7.) < LJ-CiO) II. 3 30:) =- (utt) -—u£t*‘+))'* (uLt-H) wit-0) plot-Lina 'L'hES c, '_ out) —uLt*'-l) «it-r I] Hal-t a) '1' t bl ' 1 I? we QPPIY the dl's'trfbuHUe. ProFarFy'. m * um Mum) -.- uLthuLt—r) -uLt”'-+) wthl) 4 ULt-la‘)~+uLt*|) ‘d - we as and up wHk 'powr convolution I‘ntarkls. Si[r+i).uLb-“L)JT - futt-I)ult't)d't - [Eva-drawn: "‘2’" E) ,0, ® “no @ + Sw“£1_t)‘uct- it-T)dt .. OI Q G umn tuft-“O “We I'm‘“ @ can b1 LOU-M of: inksrwh'on in a Sl'mear -, “t '1: mus’r- be bdwu—h way * = -- .-: 13>" idT— ‘t (I) £1"! for __ I -(_b_l).u(—tfil = 0 Par t4“! +916 Il'mfls o-F 'Inkjrm'bron muS'l" be be‘hfl'een "' and: 11“? wf-L—k t-‘r 3- —: 1: 4- 3 -L-£-'5)uL't-3) (9 com lag-Fauna] in on Si'ml'lqr waxy t-'+ > S‘dx ‘t'Lf—l=t*5 fi-erI-a t S I 1mm Sygkfll #1: ‘1.('&)= e'“ [um — MOE-5)] Sys+¢mizz Ebb) = ded) dd: The. impulse resPonse O‘P the overall e,qu l'S Ema), +hc alum-we 0-]: L, (t) (P3172 chum) kHz) = i[é3t LuLt)~uLt‘$)]i = 0H 53* [Sea "SCt-Si) -'- 3é3t[utt) 4402-9)] AH“) (b) To dew‘crmu'ne yL-b) when IRAN/lit) We Ccm swap -Unc order see) um ——1>-—b ——-> 3%) Since. +he F1331" syshim cam-pars an I'mPulsti { oluC't) $563)} ' (it 3 —3t the cu+pu+ is hit) = e [Mamthfl] :SL-b) n it .1. 8|? 5 t (C) Now consider Xct) =- HL-t) -H(t—IO) and Pnth 505) From Por+ (b) we Know the 001‘P°+ ‘R’T HUS) Since, the 5Y5+em is +Jme I'nvaru‘un'fj {he 0U+pu+ to ‘ML'L-lo) should be; & sh.‘{-‘-feol versron U-p LIL-b) MMIH‘PII'fid '1’. —3(t-IO‘) -uLt-lo) ‘9 [Int-m {a -- {a [At-l0) *MCt'IS? “5mg l0n¢ar|'-I-v1,wc mm mm the 4m; ou+pu+ci w U70) 3H,) -_- 53* [uLH—ULLt-S')] - e, 3 a [nth-IO) —u(,‘t"f‘5)] H.5 Elli): 0.) BY dcfi‘nf-Lm‘on the. impulse msponSe 04? the. sysi-cmtmm 9((e)=SLb) '“9 l5”, amt) h(¢)=Jah(t-'G)9C§)d’t -C9|=I For LIarl'i-Y lt'l’ ’t—S= 6- H.509) For QaUSQIHY k(q;) = O For "C(O Bid observing fihel‘mP-MLSQ; responst da+erm|‘ncd fin Par-Ha) A hot) 2 9 "c hC‘t)=o 4701' 7‘. <1 9» , %Cxc-Fore {Jae sys+€~m I‘S MUSoLl. (m For s+mbm+y ffimnlm < Go 32-? we Perfbrm the inchropl j-“ 41:“‘979'u‘3'3flldt ” E'sad’t=2.6 < on ‘3‘” 2 Therefipre We 5y g-fem 1's sl‘abfa (‘0 X(-t) a: “Lt-fl) J aj Ob) = XC'QfilrkL-b) =|n(.'t)¥-X(fb) 0-: 0° 3C£)= 2f “mayuauruarc 11] uC‘C-E’J' uLt+L~UoLt -W ~00 IO (11.5 a con+lc1 ) To ShmPh'Pj «the. inkssz We- Flo'fi %¢1’n|-c3PM0/LS u(t+|-"t) u [1—2) “UHF-c) .-.....______.——- «HI; L - - J 7, T ‘3 we si-ouri— +0 see om ova/rm? between the. The same. idea For “Mac Second I‘fl‘tflr‘ml‘, bu+ now the own»- wlnem {plat anal—i'ons 0V¢r1“P [mp occurs WEB/n it? we in’rtflra‘l'e Pmm 2. t0 {+1 when 441:. End-rafts bri over [up we {mi-(SHELB- 2 g i-d1a1[t+l~z]= 9m we +o £+1 Q. 1(t-1) —Por t2] tH 0 par t<i ‘ljgl‘dt _«—_ o-Z[t1'l"8]n aCfi—l) Mt") -—:L(t-7) {in 1:37 0 pm, 1-, <7 -— slot-r7)- u(‘t"g) W, 5 2 c t - o. u C§f_-f.1____‘._._§_(,£:I?).;5_§f::_?2 am, 1 1 I 1 II ...
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This note was uploaded on 09/15/2011 for the course ECE 2025 taught by Professor Juang during the Fall '08 term at Georgia Institute of Technology.

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HW11f08solutions - EOE 201$.“l Fall '08 ' Purl; SoluHons...

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