ece366-06finex

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

This preview shows pages 1–10. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## 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.

### Page1 / 10

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

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online