EE313 TTH Exam _1 Solution Fall 2010

EE313 TTH Exam _1 Solution Fall 2010 - EC ’21:...

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Unformatted text preview: EC ’21: T1", 1:19“ I: I. J-l-U AV-I-Jv I ' I;- 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 Thursday, October 28th, no request‘for regrades will be considered after Thursday, November 4rd 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 slide it 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. “ring; a “n.1,” eff A WNW u 4:“ ll I My signature certifies that the workon' this exam is strictly my own and that I have not reeeivedv nor utilized any , outside infOrmation beyond the allowed formulae sheets. I Furthermore; my signature certifies that I have read " I Print your name: ' __ 3 " . , , (Last name) (First name). . . and understand the instructions given below. \1 so Lion-1mg; ‘ ; Your I I N THE UNIVERSITY; OF TEXAS AT AUSTIN Department of Electrical and Computer Engineering EE 313 - TTH (16190) - Fall 2009' ' * ' :msaucaafis “ n I 1 VYOu mustcircle your answers. _ _- : All'problemsieount eduallyr ._ No credit for answers» for which nosupporting work isshown, ' or for which the-supporting work is inconsistentwithvgthe answer given; ' ' ' ' _, - I ’3 4. I ' To maximize the probability of receiving part oredit; show 7 your work and provide arbrieflai few phrases Will usually do) '_ _ 5.7 V» explanation.of.your_approach. V i i i , I l . I, L ' ‘ Problem (1); Supposelthe input-outputrelafionship of ’a/‘particular LTI CT systern is‘ deScribed by {he £0110ng difl‘erential equation: “ ‘ ‘ ‘ I I l _ We) + Hymn? '+‘ 64y(2) = Ma) + xa) Find the zero-input response y0(t), subject to the folloWing initial conditions y(0) =72, yw(0) = 12». lithe eigenvalues are complex, you must express the solution in the “standard form” given in class in order to 7‘ V receive'credit." “ v _ cw; ETD-=5 Wu. law. 64 :— 0 m> Lh’fiyi: o ‘ Lam; 4“? ~9 30/ C\$;-.-329 v, - { 3,, (b c‘ (— Edg I 4— (lag 4. “$5353.63. ‘ ’i ~ W ' I _"___r jag-1: ‘ __ . -» v_ r . - \30, A6716. wrte (I909:— (aahdfi'fi ‘7pr etc “25 l J: ‘Co’f‘ WKAL‘du "HACL Sckmg-fcnm ' .ipéééwzbflanw , a ' ‘P‘rrobleLni (2) Consider CT SYstem characterized by an impulse’response- given by, , I ‘ V .l + -6t¥ I ha) .— 4e um Calculate the zero-state fesponse y(z‘) for the following eicitation . “dew #31429 8((‘\ 3" j M I " In; MW) . - - Lama: flaming—4943 '34 (twae . u I. ><¢7~J wt—»E\:c§)ua+\ 4e. ' uti-~’t3 Cit ~=> «‘—=9—--:?~',- gnu: ms 7:,» 9.». . ‘ .fi. .91- 1:45.» 37:0 It; . , . \cu-X-M L( (133 euka3~ Klf‘ifl “A ## *w H "W M ’7 A 7 H A# A N E #7 “A m “7326* " ’ Problem’(3) Find and sketch'the even and‘odd'pa‘rts ofthe following signal, ' , xm = mar) , , p _ . ; Wag = 4i: u t—~L—\ ‘ To receive credit (1) your sketch must be consistent with your analytical expressions for the even and odd parts, (2)-the coordinates of all important points must be carefully labeled, and (3) the numerical ' ' Values of the slopes of any straight lines must be indicated. , - , .__._7Vl,;:..__..__;w_r fitw~fl~n .7 XZLAA—s J; Kate: +3 sat—4A atomiih . g =r Vr'iquthxrheflitvt—fl . ' 7*: 7 ~ “A v 7 A g M u ‘ W 7 ‘7 74/457 " 'kPreblyem (4) Find the energy and ’p‘owér‘of the following DT signal, ' ' ' ‘ ‘ 'x[nJ —= sell-W] Numerical values of energy and power are required. \ I—nh- . v (“‘0 BEA-1:55“ A V in] :y —3 Ahugni lxgmlél C} umil 7 3}“ r w \xtv‘jlbz‘i '_E?Z V‘I:-°¢3 ?- CH-Cu—‘R «flu—“M2. J: “W. —L {@4693 +444qu q " W Hsl—l-o mis-N-1 ‘ k U l A l ‘7 376W Problem (5) Carefully sketch the fim'ction'cCt) where the asterisk denotes convolutien‘, ‘ ’ ca) = 527260 * comb(t/4) To receive full credit, it is essential that all important coerdinate points in you; sketch be carefully. labeled. r 5 4+? ( .3 ‘1.) We (3% => k .L, 3 '33 *n\ .39 .YS'zu-ob =5 WEN); _._.-. ' 2 Ar SH: 54MB M=~w Ac “5 —}_—: 3 Mr H“ \ 3 ~— ._~ fi‘rfi'awglzj '5Mk-A5A5k ' ,/ "0“3‘47‘5Jrfil3‘a *— ambit/Lo - ‘ ob . pagaéfars" —_ 4 ‘ . ‘ ,1 4rd (2» 51%, 9. 4m 77 t :51»), elf f-i 4" *4 " ' ” "' "Tr-“C 4mg Liz). "tux—Ar t“ ‘ E‘dK‘A‘J.‘ 4e» 20 2=+H<sr<bm ~ h:ewe 4* 3/33 » ' ' lgtg'mivggi: K , if“ 4H: m 103:] v w' ._ - V _V _ v- 7 _ .WV 7... V“ 1v._ .-__ 1 ’ whemfin:o"l=t-hx_t3 :‘lévw { V . ..,. ) J IJ. _ I 'TH'EEND ...
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EE313 TTH Exam _1 Solution Fall 2010 - EC ’21:...

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