11FMT2SOL

11FMT2SOL - Midterm #2 of ECE301, Prof. Wang’s section...

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Unformatted text preview: Midterm #2 of ECE301, Prof. Wang’s section 8—9pm Thursday, October 13, 2011, EE 170, . 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. . There are 12 pages in the exam booklet. Use the back of each page for rough work. . Neither calculators nor help sheets are allowed. Name: " ” Student ID: E—mail: Signature: Question 1: [27%, Work—out question, Outcome 3] 1. [2%] What is an “impulse response”? 2. [10%] Consider a system with the input / output relationship being y(t) = (1:0 x(s)e—2t+2sds> + ([0 $(s)e2t‘2sds). (1) Find the impulse response Mt) of this system. 3. [15%] Let 2(t) = etLl(—t). Find the convolution integral w(t) = z(t) >l< Mt). If you do not know the answer h(t) of the previous question, you can assume that h(t) : L106) — U(—t) and solve w(t) accordingly. You will receive 13 points if your answer is correct. Impuim msi‘ohu is firm OLKTPU‘E oi)” m gfiflsuw“ WM" '15?“ lbpu‘t is an impul‘v‘ ‘ (or became) Ci) {3% Li] w Late—M .. ’1 tings J ‘ t u (g thl = I saw st “" cls ~+ 5 (its) t m z:- 3 ( firat ripe /;}l’bl 3‘: it, 4 O ? E j, r 2‘» to new} $4359) fl l“ _ V cmfii’i‘wl’ M 0 Mg .1 WW N w < fifi 7Q; «:33?» “2;? /@0 I, ‘ ’ F {:3 a 7:: “’3 m” fi§cfiifi ‘53 i “Q “a it raw N flag” WW F W “A £0? flag WEEK w 3W fig; r 4‘ wl fig... “199$ i «a, M» 3 {3 h ){r awfl} W Mk ‘3” Mg) WQC'Ifil: M A“) 2; g, (shill; “F .3 CT}, ,1; S so as; U93 “3" ( ,0, 9/ ,4 To, 14;; / 3 29%: Q 1:; Zn; will; it“ ,4 i; A 5:15?” 13 gin”? W ¢ 32 + «aw <1" 32 Z? t $11: fl fig. Q was; V 3 )g/fiwfiwfifir (/LJCt’) f" 3 Mfiifi’; if 51% 2:“?0 .hftgfi h m) m m: é W m (“fig Mw~w4~~ww Mg Wan/we “fl {flag :1; i w.‘ W w 35%) Q «3, {fing {fing} W LAC“ flfiwwi; E ) “ix: w “9Q” 04 ' Lucia) “' g M ya V” “Z; V €33 / *5" '3 “fl // I «a fit! ’3 “Z” “42‘?” ’2 f: Cay‘) ma a WE #3 wk“ < Mafia «SHIV; ) a“: < p“ '8’; a} "fly 0 g» M P Lfi W (‘m “a; V. will”? Question 2: [14%, Work—out question, Outcome 2] 1. [2%] What is the acronym “LTI”? 2. [12%] Consider a discrete—time LTI system With its impulse response Mt) being e‘fit i W) = { f 1 St (2) 0 otherwise When the input of the system is :z:(t) = cosh/3t) + sin(t), find out the output L;Nw / TrW— Ihvwm'ant (fifi “H (W) 3 j If "3’ ‘3‘” wt 6 5LT: "3 '” r - w" t _— 15? may; ., CJE +5 w”) « a 5% + 5 Lu) ,- Tl , ’ C 0 w 5L. ( j I ,L a ingjgsujuo) {m a JE+ pw ‘1 V .— r i ‘ ’3‘ 5 at: w (“33 ~+~ .3 5E J t 51:“ C f3 ) J; ) I} J}: v\ ,1“ ),.:;.' 4 ‘ r b T + k ; fiflw) us 3 ) ‘ ‘ . r ’ “ff”; m a j ~- C J???" ‘+ J i) a I: i, [Q fl w 5* W7“ ~1- L”... M7 :31) OP 3 $1.2) J5 \) 53 *g‘ j if"; E k a e w uMD t 3'; £1» 3 \ d w), sis s“ 7/1 3 L 49 * My )1“ «Q, m9 g) ‘3" i5 § 1: 2;: n S? j M j» :2 L 3“ “ 3 / fig” is; g) i w: fl” 1 “B i: J), xi” 4/: “WM' ‘ “ Q: W B a} M k V y. w m f”? ) mfi ‘ ’3: :r c Question 3: [25%, Work—out question7 Outcome 4] 67m 1. [10%] y[n] = cos( 7 ). Find the Fourier series of 2. [5%] $05) is periodic with period T : 4 and { Plot a:(t) for the range of t = —6 to 6 mt 008(2 ) fi—lgtgl filgt<3 ' #0 3. [10%] Compute the Fourier series of Hint: Consider another signal: z(t) is periodic with period T = 4 and { We know that the Fourier series coefficients of z(t) are 1 0 fi~1§tgl fiigt<3‘ uk=0 fik¢d You may want to use this fact when computing the Fourier series of J (4 fin/“?) ’Qw'rj Cérmh/M’) ,1 5 ;”\h ,.. _ “i” , in); 4:05; C -W ) M “QM r, @ 7 Wflwwgfww :- (___.~; m‘iOCi a "-’ i W 7 Pace—“mi “’(Qms) ‘fith 3 fi‘ 7 I H. “m f. a l ‘ E 3; J, ‘37 (“is 7" 0‘ K M ,(fmxw‘iw " O (:9 3,. 3250130”; 52" M my 5L, 4 711:7 a: ' n (as ( .3. ) 'Q, Wfiai+ t£”“‘ ;/\ g ml ‘ t]? Z 3 (3 Question 4: [14%, Work—out question, Outcome 4] We know that if x(t) is periodic with period T = 4 and t+1if—1§t<0 :c(t)= 1—t1fogt<1 , 0 fi1§t<3 then the corresponding FS coefficients are 3; ak —_ I ~ 005 E1 I2 2k27rg2) Answer the following questions: 1. [7%] Compute the value of ZZ:_OO oi. 2. [7%] Consider a different signal y(t), which is periodic with period T = 4 and t+1if~1§t<0 1 if0§t<1 2—75 iflgt<2 0 if2gt<3 Find the Fourier series of y(t). a l M <23"; '3‘ ’L‘ C «if: ,{q ggl‘fi; "i" ‘3 6 \ {jg/t“ 4mm“ » " w» l C.) L3 '1; W" d“? s- 3 W i g m w» 1 gym , :3 a . V ‘21» 1 MN A r E 4 / W; J“; L 49" "W‘ 0 , f w» 5:7 "D l we» I if Q‘g \ WL 5'? i l A l 6 "2g K it“ s A; i ‘M (M M [,3 W 34 E» E; l X «A E E“ M if“; ‘“ M (:1; 2; Mr W “i; “#4 \ fifgflfi: “on g “Q u 3,,” lwfi~~z an“ g: L g <5 3 0 w" *3 v, 2 Ear W “J; g 1 $2? “fl > “i; Question 5: [20%, Multiple Choices] The following questions are multiple—choice questions and there is no need to justify your answers. Consider the following two systems: System 1: When the input is $105), the output is _ [foo $1(28)d8 ifO gt Wt) * {0 1ft < 0' (9) System 2: When the input is $2M], the output is 3/2 = min(0, x2[n + (10) Answer the following questions 1. [4%, Outcome 1] Is System 1 memoryless? ls System 2 memoryless? [\3 . [4%, Outcome 1] Is System 1 causal? Is System 2 causal? 3. [4%, Outcome 1] Is System 1 stable? ls System 2 stable? 4. [4%, Outcome 1] Is System 1 linear? Is System 2 linear? 5. [4%, Outcome 1] Is System 1 time~invariant? Is System 2 time—invariant? NC) r i N O / N (:3 :22 l“ C) / v’ its: 3% gm ff) 5' it ~ y E; g N y «5 N a) , 1,3???“ e: ...
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11FMT2SOL - Midterm #2 of ECE301, Prof. Wang’s section...

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