quiz1asu09_soln - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL 35 COMPUTER ENGINEERING QUIZ #1 DATE: 06/05/2009 COURSE: EOE 2025 NAME: S 0 Cu 44;: m STUDENT #: LAST, FIRST Recitation Section: Circle the day 84: time when your Recitation Section meets: L01: M 2:40—4:25 (Taylor) L03: T 10—11315 (Chang) L05: T 2-3945 (Romberg) L02: M 4:40-6:25 (Verriest) L04: T 12:00-1:45 (Chang) L06: T 4-5z45 (Kornberg) 0 Write your name on the front page ONLY. DO NOT unstaple the test. 0 Closed book but a calculator is permitted. However one page (8%” x 11”) of HAND- WRITTEN notes permitted. OK to write on both sides. _ 0 Unless stated otherwise, JUSTIFY your reasoning clearly to receive any partial credit. ' Explanations are also required to receive full credit for any answer. a. you-must write your answer in the space prOVided on the exam paper itself. Only these answers will be graded. Circle your answers, or write them in the boxes previded. If space is needed for scratch work, use the backs of previous pages. - Problem 01.1: (8 pts each) Each part of this probiemis independent of the others. (a) Let r' be a real number where 2 < r < 3. Find and plot the complex vector (1" + jr'P'. (37/1. 45 hr) 2: ' 2%“(H9Mb :: gnu—“6C J J 6’ m/q, 15'5“" . . = m/ + A»; r I“! V : A + % V“ Z a 2% V w.) ) 2 J M m 4 (b) Find and sketch the complex number 3' cos (9) - 3613(6) where 6 represents an angle in the first quandrant. r +17 f2, 6:9: ws(®)+/M9/ ' [a r ' 9 _. ' «9* .9»; 0— ‘ f 8 3 r 1‘05 a ll '3 ’53 f S“ (d) For P = (—3 + j3)ej“/3, express Re[PejS°”‘] in standard cosine form. r , rrr "“3rr332 4,2crzc 617%67 “/3 W) W W €7'-’%zn— r 347% fldfé‘é’gfi’rcio / 2:" 4’2Q2G Cos(é0’77_éifi' reef?) “M” N, ”Lg/9‘23 3.9%“ t Problem 01.2: (8 pts each) Parts (a), (b), and (c) are mutually unrelated. (a) Express 12 cos(607rt + 1r/5) + 5 008(6077‘! -—- 7r/5) as A 603(th + @- A =_’__q:'_;_;: J ()5: EU} we =_&Z (in radians) 7‘! )fd. a? far}? ) {26 3‘ s56) :rwmre (b) Sirnplif}r the following expression: .? m(t) = i cos (32 85111 + Eat) 19:0 4 You should be able to do this without doing any explicit calculations! Sketch the phasors associated with each of the terms, and give an intuitive explanation for your answer. “MVeJMIM/Mfr/ ”47;, e fa, .._.. & /,‘l'e.$3-’n, L \l (c) Find the fundamental frequency (in radians) of sin2(27r60t) + 3 sin(2¢r6{}t). . - W - .mr j(c7hm6ai_€ 2347601)): rifeyzmmic, 7‘2? 2) :: z231(2 warmtyz):z_ , sway/mar) Problem Q13: (3.) (8 points) Sketch the spectrum of Re[8€j7{t+1) cos(487rt 1r/ 3)] in radians/sec. 75‘" WA7 =71 fir-I?) woes- EEK/*2.) M/fi/ 5p flux/y?) cra‘J‘iW/s) ?f,(?+77/J):é’ 9e “in/g) (i W wen/W qwezr' quT-e 957”?“ (b) (8 pointS) Ebcpress mos): cos(10281rt + fi/4)cos(2561rt+ 17/8) as a Sum of two cosines 5* 93(1) = A1cos(w1t + (251) + A2 (303(th + $52) 5 @QJ/(fi %/ = (“2 8 %.{E1 radians) ’ d- ((3350; 47$) “i 'i m“ We; 75/ E? I [4: .19 fi‘ || VJ .:‘ \ 8‘ V2 mfg w _‘+'n_7_r (in radians) (e) (12 points) Suppose 1116): ”(27‘8” and a:(t)— .. —5 cos(1!;(t)~ 9 35). f {:11 .‘L f." (i) Find fm-(t), the instantaneous frequency of 330:) in Hz. W” C E} " " 5L .. 1 /f 9 1 wfif’wmi’f} We W 4'3me 2/ ¢{{/-—$yu @7801?) e . 721mm {,1 Mr; A “"43 )7! it}??? mfifl/zyf (ii) Find the fundamental period of $6). . j .2: m 1.. (d) (8 points) y(t) has instantaneous frequency fyI-(t): 3151'!2 + t in Hz. Express y(t) as cos(C(t)) where ((t) is to be determined. ...
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