MT3SOL - [‘3 Midterm #3 of ECE301, Prof. Wang’s section...

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Unformatted text preview: [‘3 Midterm #3 of ECE301, Prof. Wang’s section 8—9pm Wednesday, November 17, 2010, WTHR 172. . Please make sure that it is your name printed on the exam booklet. Enter your student ID number, e-mail address, and signature in the space provided on this page, NOW! . This is a closed book Exam. . This exam contains multiple choice questions and work—out questions. For multiple choice questions, there is no need to justify your answers. You have one hour to complete it. The students are suggested not spending too much time on a single question, and working on those that you know how to solve. Neither calculators nor help sheets are allowed. Name: fa Atng Student ID: E—mail: Signature: Question 1: [25%, Work—out question] 1. [10%, Outcome 4] Consider the following DT signal: ej“ if0<n<100 Mn]: “ -.- . <1) 0 otherw1se Find the expression of X1(ej°"), the Fourier transform of 1:1 2. [15%, Outcome 4] Consider the following DT signal: 100 $2M] = jsin . (2) Find the expression of X2033“), the Fourier transform of 5132 Plot X2(ej“’) for the range —7r < w < 7r. w n "a '1 - Iv" I” J((’0) " X/M = 2: mdev‘“ r 2: e) 5‘) :z@ / ( p.=—°é A20 [I Ac” .(l‘l‘l)/0/ 4- ((-9) 7.- -_ -U/ LIJ ‘(Irw/‘(zal : l” e) ( j : e) 2. ~ 6) - )"V '1 W] J W _ w, ( C Cad! (CVLN / __ €40 / It w : ){I—w/‘Z" "2J5’”(Lai‘l{” V : ij—u) {In T (' // e '5 “(Hz—w!) C “(H/4W . W leeJ7=j37Zk§iHU~ evzw 4’ Wm; Md 2 #71; [gt/5,, £357/Zré/ +ffu+ 4,1749%] k:— ,0 Question 2: [25%, Work—out question] Consider a DT LTI system, for which the in— put / output relationship is described by: 6y[n] + 5y[n — 1] + y[n — 2] = 7:5[n] + 3a:[n — 1]. (3) 1. [10%, Outcomes 2, 5] Find out the impulse response h]n] of this system. = (—1 3 If you do not know the answer to the previous question, you can assume Mn] 2 6 + (—97%! + (1/4)"U You will still receive full credit if your answer is correct. 2. [15%, Outcomes 2, 5] If the input is 3;]22] Hint: You may need to use the tables. )nU]’/L], find out the output i. t w “wk/mi? + a“ W= 7W“? * 38"“X/W'V New“ +56in tau-2‘7 = Xtejw/(77‘J’CUU/ . "U 3 t ~) 7,43 U 4.4] + _ HQU‘M ; — —-~ 2w“ XQJ") (316-0 )(zfea/ had 6 MUN”) r Wife ’7 z 77‘ 30"!“ - fl = «2 2474657 3:3‘A At; Ari: = 24r3{3'/U>7 B" Nil/[744:7 Mfr ) ‘4 - #2., PL ' "%[n <—-—--/5 _ -‘o./ HM — 3+c-Jw + ugfljw AM" 4' / deJ : i .._L—«_ #1,? '4 , i (—1 M112) r g "ii/"WU 3 H1153 T 3:, #31ch A j 3 3 -u I v div [JV - 3 fit": 2 Xlel ) : (gel/V ‘5 j'me X6 (2 63-")(37‘ev'72 WV“ Haul/(New MMeu‘wg-aw) + Mow-J“ mil“) + C(Zrev"? = 2/ it re?!“ . K s , C : é 74+4/3 +1631] g-A C 94 Ez-S M +55 f6 ‘~ ? MHCW/ MHW'Al—‘l/ A ,1] z a Me -4 numb/nu A=3 - 3 ~3 6: w :x. —-——« w m ) 2m" 'L He‘d“ ’9 (3+6‘JV)‘ , a M HZC'JV (+316)" + 3 ((+j’e‘d‘71 fl“ 2 §{~;’j"%}- 39%;) + §(h,()('—3L)”M«) :2 ’3 I I l Ala/am Lam KW MJ—‘MJH‘s'V‘flH"WW3] I I 3 ‘f H 3" 511+ s + . _ -- (e ) “few /'?c"1" l + 3fcduf Y-eUV (3*e”J'”/(°‘{-c75“’) U = : ’2 +evvu5'J-l‘“ + Q Java/at [2 +167!” 36 + 2570 new" (3%“ /( Y—CV"/ {zfe’d‘NY— 67/“) Hawk/«(WWW m4“ *ZC'JUFc’Ji‘V J: W” f w? (‘l—[dwflh‘eUW/l ' #57)” New” [We-0272 Mme?“ r W 12 way? + mm = w + 7/1r ,L/ZBM/czzay 33/4“ 6:7A’3 4/4 #3 -C = a, W 2/4 ,u/szz 21AM” —/2='?l A —/3 vs 7A ~c=3 774:” :11 :fi r—u - 1 A47 ‘ ‘7’3="‘%”':7 B'fig’iwz—gii 5v ; 132,—“! ‘ 3/ I. ' ) Y’a'dv + ‘1? JfC-KJU + m!- : a I J, v7 I 1 -150" ~' — I. W ’ red ‘17 lm‘eJ" * (15.9w) 7t?) mil/41%) +23% 312%») + («w/H “WW [A Question 3: [20%, Work—out question] Consider a periodic signal $(t) of period 27r and x(t):{1 if|tl<g (4) 0 if g g It] < 7r 1. [5%, Outcome 1] Plot 3:05) for the range ~37T < t < 371'. 2. [15%, Outcomes 4, 6] Find the expression of X ( jw) and plot it for the range —3.5 < w<3.5. x/f) I z‘ — “L” '7 1 t1 1 . “Jo/ii” 117 z "7 ‘5 1 7" 1f 47 91539”. F'réf‘ J?/,(0J ’ I 4’ I 7' 31,3316 / 3? ’14 J. 1 7/./‘6 f M” ,, XH/ed Jt ~ 2” -17 6” Jr -‘ 2v Jr 6 ,f, ' 1 i L’- . 5;n[€é/ :3; J1 C ’ 6 ' 17A = Z'rrkZ— 4M]le fif7U =-.a 2 .« J? :erl 5_’"M{L/E/f[v-227£/ p won 77k ~d 90 Question 4: [30%, Work—out question] Consider the following signal 33(23) Whose Fourier transform is w+100 100—w 0 if—100<w<0 if0<w<100 otherwise X (W) (5) 1. [12%, Outcomes 4, 5] y1(t) w < 200. 33(t) cos(100t). Plot Y1(jw) for the range of —200 < 2. [3%, Outcome 4] Compute the value of ff; y1(t)dt. 3. [3%, Outcome 4] Compute the value of [:0 [y1(t)|2dt. / 4. [12%, Outcomes 4, 5] y2(t) = :r(t) -jsin(50t). Plot Y2(jw) for the range of —200 < w<200. .7 C EON/(4,416” 7" LX0/Uf(fl// [10“) 5'0 _Lou ~(0(1 {60 100 , « a0 _ t 1' (wt/F], wig J” J: Y/(~0): j“: fili) Jt :0 ‘w - z . If {gm/Vt " /IV,/eJ“’}/ Ju W new” a ’0” ,L ‘a[ viva, ‘7 W flame/‘15., fgéflafl’VJLJu/J ‘777 [/4017 U My JWOZ M0 0' J J Z(.’V3+1ao<xz,L/g"4// +(/g"4,—/00u‘ “rm/N ] 3 "(M (I :J— ‘177 l 6 6 6 ‘ J [L6 ~ é 3;)”“13‘2‘ ’L ’oé'mohpac'm ’L LJQU'YV 3 M ‘ -«i I , a :MGHW “WW * (Md/W W 1/ : 11/06] : “(—0: ‘(n’ 117 /00 (/0 7- won/z c 6 e M M? /—/0 40 1"; / ...
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This note was uploaded on 02/07/2011 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University-West Lafayette.

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MT3SOL - [‘3 Midterm #3 of ECE301, Prof. Wang’s section...

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