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EE313 MW Exam _1 Solution Fall 2010

EE313 MW Exam _1 Solution Fall 2010 - 4~ A m” “1.41 EE...

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Unformatted text preview: . 4~_.._ A m”. “1.41 EE 313 Fall 2010 Solution to Exam #1 Indicated below is the regrade policy as stated in the course syllabus. Since, the Exam # 1 was returned to the class Wednesday, October 27th, no request for regrades will be considered after Wednesday, November 3”. You must clearly indicate in your written statement where you belieVe an error was made in grading. Staple your written statement to your exam and either hand it to me after class or put it in an envelope with my name on it and slidefit under the door of my office, ENS 342A. The following is an excerpt from the course syllabus Regrade policy: All requests for regrade of a homework or in—class exam problem must be made in writing within one week of their return to you. No verbal submissions will be considered. The purpose of a regrade is to correct any error that was made in grading; therefore, in your written statement you must clearly indicate where you believe an error was made in grading the problem in question. Please note that if, in the instructor’s opinion, a regrade of a problem solution is warranted, the entire problem solution will be regraded, not just the part in question. ~ 3‘4l'3'l l v5 . “*1!"va 4. 1‘“ - #44 444 , Page 1 of 6 Print your name: , ‘ ' , ' (Last name) (First name) My signature certifies that the work on this exam is strictly my ‘own and that I have not received nor utilized any outside. information beyond the allowed formulae sheets. Furthermore, my signature certifies that I have read and understand the instructions given below. Your Signature THE UNIVERSITY OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering HE 313 0 MW (16195) - Fall 2009. Exam # 1, October 20, 2010 Instructions 1. You must circle your answers. . 1. 2. 2. All problems count equally. 3. 3. No credit for answers for which no'supporting work is shown, or for which the supporting work is inconsistent with the answer given. ‘ 4. 4. To maximize the probability of receiving part credit, show your work and provide a brief (a few phrases will usually do) 5. explanation of your approach. .._._..._..- "mm; 1/6__.. ._.._ v r . y . . ‘ v, . 1 ~ ”f i Prob. 1 Consider the periodic .signal 75(19- tshpwn below. The period' .18 three. (3) seconds. Calculate .the energy and " " . " ' :' ' - - poWer ofxa) . . . . -. :- ' Problem (2) Suppose the input-output relationship of a particular LTI CT system is described by the ' following difi'erential equation: (”(0 + 15y(1)() + 60y(z‘) “wa .2360 1 Find the zero-input response yo(); subject to the followmg initial conditions y(0) = -J ym(0) 1 8 If the _ i eigenvalues (roots) are compleX, you must express the solution in the‘ ‘standard forrn” given in class 1n ’ ' I order to receive credit. thqrucfi—Lntghg'cflEzua‘i-eum =2 “(LA—H98 4“ 6&2: O 01‘ éK+tg>KY+GB2D CV10?“ c,¥2r‘1g\—z¢— Pool‘h (QM-g ¢VK'\IO.K\J~¢AX 1) Fl 2 - lag) Y m...— (C) [ gas-1+1 =1 c. é: ”*1. egg“: AP®\'j 1w Armani come)“ 4.;ng ' 30(0) 3: C1 'Te’l 38" H 3W4): c (”chem H Jrcic— (9‘12 Ti'}5")(o1 i—x 0. C1- 452“ ‘3’ ' '.TLIao gqf.gg¥:oz:t£} fLuzio ,umkAao'sfiL/‘J " C1+cztr .17 H~LUC1+IOC1:'IO ' ' 7‘ £11.... ”.11 \Dom cow 1% E" . 114—11112. 2.»:an 1L 7:314 garggjr Jr’D ””91 QQI‘JL “H.112, ‘ Page .3-.9i§ Q; . . . > Pat/\PL 9%. 3C? "(2'9“ wk‘cm‘lkfi... ' V ' i V §é\u~\- am 13 VGA Q1WW”WNW—WW"WW“«HNWWWH T 1 _ _ a -._ 1 _ _, 1 _~ _ .c* “M h _ _ _, _ - _ _.;.;3:/‘5 ._ ,J_lll_1 Page 4. ore - 1 , Problem (3) Carefully sketch the even andioddeartsfof‘the:foll'owing'DT-,.signal-', - ~~ ; t ‘x[n]'=~;~‘eee[n-2j ,. - ' To receive credit you rnust not Only carefully label all nnportant coordinate points, but you must also provide some indication as to how you arrived at your ansWers, i. e., no credit for juSt providing the g ‘- requested sketches ‘ ' ' ' _' ‘ ‘ " " ’ ‘ ' 1 .1: V v.2 Lf+LYV1 1 g i -__ ___ -;__ , _- _ 1 __ ~ 1 _ -1 H» _ _,, V_ _ - ,_ “4/61..- 1_-_ Problem (4) Consider an LTI CT system Characterized by an impulse response given by, . ~ My e’4e‘6‘uw . Calculate the zero-stafe response ya? f0]; the following .eXCitation, W = ~3e‘5‘ua) gxte‘x — \ =1Vmo ova—Hap , ‘- -‘ v .i'lg'I—‘g; ' , ' . :olsovao eme— 6‘” 30$ paggsofe ~ ‘ .- MLJ LT Page60f6 , § 7 Problem (5)‘Deter1’nine the numerical value of each Of the following two integrals. < 'flo :- ' f _ 6(2t—1)m( - . 16., . 4 f (10711176) sinCZ'irt) cit O U V 5 SllffiHerl-Eli Si Sit-E «3 ”EV. (5‘5 , , guo Cc“ _ (0 ALL't‘) Ari—9V2: « “ 2 “36%) l Si+4>m>é=g+a (a: [1. lb." .. J. '2. ‘. .Qa -._ .0006 ' - co ; . ,1 h “Sailfish/kl: (%)“§\‘h (2‘74535‘3'1’: g E S( :L‘WD $1ln(’1fif> Z S §(1l:fy\3 $‘M(z; g_a.{‘q fl. ‘5; ' ice 1,3,1'" ,. “.rm'i'i'l. VJ" l ,If ,'f'f'.' . wufl-f 4L+ *2: K— —~, 2 cs (f—M S‘m (am) on— H L THEEND fl __ l - _ - We _ H-” mm-m’mw A N, _ l “W” w W a _,;6l_6,_ fifl ...
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