ece366-06finex - Name: Stadent IE: ECE 366 MNAL EXAM...

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Unformatted text preview: Name: Stadent IE: ECE 366 MNAL EXAM Becamher ll, 29% No textbooks, notes or HW solutions. Two pages of hand-written notes. Calculators are allowed. Exam is 2 hours long. To maximize your score on this exam, read the questions carefully and write legibly. For those problems that allow partial credit, Show your work clearly. s Good luck. 0 Q Q 0 a Part A- {25] Short answer questions 1. [9] For each given system, circle the appropriate system characteristics. No explanation is necessary. ‘Ia Nonlinear Time- ime""‘~~i . . \_ Invariant variant Nonlinear Time- ' N Invariant - . E if i: 2% 9; it s", s s is =2 it ;{ 2. [6] Consider a. discrete»time LTI systam with input x[i’£] = 90587]??? m :2). Dstermine y[n] if the magnitude and the phase response of H are as given below. Simpiify your answer as much as you can. Hut}; 3. {10] For a sigma} 95(5) , the magnitude and phase of its Fourier transform) X(a)) are as given in the figure For each of the signals below, find the matching magnitude and the phase plots from the ones given below. No 6X§lfififii§fifi necessary. We pas‘ééai eredit. Signal Magnitude Plot I Phase Plot I x(~t) D x(t - 1) _ i x(z‘)ej’" ‘4 E- x(2t) {73‘ :x(n)§(t ~11) €32 PH Ase PLO T3 A muff g Trim ‘ ‘iT e+rw . on w 4 , C ' “ D (35“ Part B Show all your work to get partial credii. 1. [25] A causal diserete~time LTI system’s input output relationship is defined by the foliowing difference equation: 1 }’["]**y[fl‘2]=XinW1],y[—1]=1,y[~2]=0 . . , I 9 I? ‘éfmé are} a) [10] Find the response of this system to x[n] = 2u[iz] using unilateral z—transform.’ b) [5] Find the transfer function for this system. c).[10] Assume that the system is stable: i) Determine the region of convergence (ROC). ii) Find and sketch the magnitude of the frequency response] H |. Hint: cos2 (Q) + sin2 (9) == 1 M .742“) gig->3 e" View as His“): e" : l 21%: m2? ._) ,—a 3):} ’éig 5“ g: 1’: “z 9’ 34L ale-w ’Eiqggé}i§jfi$ ) yup) )1 Q I Be}: C @3261/01 3‘ i F “((9,33’” 3 #é'éfl—fl : i, wgizdm .Uginl‘zm it“ I I (cosl2A1§~‘l,g{3 gens/242.)“ 1 5.5.3} “it; ecu-Mesa 933$ i {i%%~%2—~l\) ggqu—wflfliefl e {NE "’W me Extra Page Eb? Qaesfien i: Hz") : 101% "E “W 7 Q3%~»s)‘3H§ «2’5? :5; 47 K2. “5‘; V3 3%-3 Blavw {xi-«vi ..__ {q WE K5 Ki :3 a ,g 3A; {2) Val/:5} WW3 _ («539% a. “\Ci ‘3 . KL» “,3 1 f: “2.2/3 : WEE L‘ ‘ \Vq b2?) Mug) 8/3 5* {<3} =— =i£ U M4 \Hfic—«w 3— »LE +§i 3 95.4% £55.33 (199;) 3"% zph 2. [25] Consider the discrete~time LTI system with impulse response Mn] = 6M + 1] — 25M] + fluted] 5 shown in the figure below. This system acts as an edge detector. an. F—fl gin] ,<\,f:*)___fl ,,._._,,l Hint g ...... r, ya“ ‘ I Lkflm *WJ E D [ m a) [8] Assume that d[n] = 0 and the input to the system is x[n] = u[rz + 2] — u[n — 2] . Find and sketch the output, y[n]. b) [5] For the system in part (a), now assume that the noise signal is d [n] = —§[n + 1] . Find and sketch the output, y[n]. c) [12] In order to use system h[n] as an edge detector, we will add a smoothing system h n = 5[n +1 + 25M] + 6 n —1]before applying h[n] as shown below. For the signal in part (b), find and sketch the outgut, y[n . s[ ] ] t ttl WQHMM 1—» Din] xtnl: i8§0t23+gfiqflj igffjj 45)]5‘43) «K x w]? "be i W 1%“ 1 Km] tight—H] * ngnth STi/xwlx f ><Cn M1 «— ZECYHJ + t] t, 433 +8Yn¥aj 3%“? +8Ufl b éigstm/zs « aside] «~28th ~28Yn43 I — «z 4 8M+13 +5)th +<§Cna iii??? haldkgtflfd \4\ '2; ~t s1 ~— gtti—t 23 as ~; gtto YEM h] ‘ :eggflé’gg “V by (X ij tdtfldv ti “Ml . 3 i: ( with : Vii/EM JFWYQ uh eta A g P w +2. ~~~~ mtgflggflesjsgéhstzggé tin “E3 “th it] “‘23 é gm 3 45]“53 “‘ngw’fl “t 4'35?th ~smt~~stimitewj§ «t 2g teat}, .~— $th W I ‘ ,/ I?) HMEE 2% {Em/$5 ‘E‘m wk E {gay} $2?” $33 {$351th 3. [25] Consider the periodic continuous—time signal x(i) : leos(207rt)|: a) [12] Find the Fourier transform ofx(t) . Sketch the magnitude response. Label the amplitude and the frequency axes. sin(x) Hint: sin C(x) = x b) [5] Using your answer from part {3), determine the exponential Fourier Series coefficients, Ck , for x0) . C) [8] Design a filter with frequency response, H 3 such that when this signal is passed through, the output is 608(807z1 + 772) . Determine the magnitude and phase response of H . What type of filter does this correspond to? Hint: There is no uni ue answe . q xii—‘2 ; el‘oi’le—ttg—QQQWQ uo‘tt sort won" jflzQ $\‘€\C tell/Q} tngW/aj‘) . _ i+ .3— ‘W i" ” like 3 {EW‘XC £W723 Jr etn§i§éfigw =5 figqéf .— '5 W/g‘s ‘ . i _L; w_L§ “ W2 Tint: & :35} i , Vi ‘ a “it ,2 “if Z. ink ‘ y M y” " if E t g‘t‘gifiet X “so “an i we 5"? Extra Page fer Questfiim 3: 105 C%; \ GWUJJQE Ta 2: 2G ggqarflz} a w de WW WEW Swim {ST/ks A4 wage“) % flausimfi‘? W5 T"? {3' $50”??? “'qu ...
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This note was uploaded on 06/08/2009 for the course ECE 366 taught by Professor Staff during the Spring '08 term at Michigan State University.

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ece366-06finex - Name: Stadent IE: ECE 366 MNAL EXAM...

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