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test1-summer - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRlCAL & COMPUTER ENGINEERING QUIZ #1 DATE: 01-June-2001 COURSE: ECE 2025 3...... M, M g!!! LAST, FIRST Recitation Section: Circle the date & time when your Recitation Section meets (not Lab): ~ (Tues-Noon (L01:Bordelon!) Tues-2:00pm (L03:Bordelon) CT ues—41OOpm (L05zBordelon \ , .. “fie, I Thur-Noon (L02zLi) Thur-2:00pm (L04:Li) “* 0 Write your name on the first page. DO NOT unstaple the test. 0 Closed book, but a calculator is permitted. o One page (8%" X 11”) of HAND—WRITTEN notes permitted. OK to write on both sides. 0 JUSTlFY your reasoning CLEARLY to receive any partial credit. Explanations are also REQUlRED to receive full credit for any answer. i 0 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 provided. If space is needed for scratch work, use the backs of pages. g2? Problem su—Ol-Q.1’.1: Four different sinusoidal signals are defined by the following representation : ’ (Lune — “/5 (a) :L'a(t) : 66_j7r/3ej4677't + 66j77/3e—j467rt [3 cos (b) xb(t) = 6cos(467rt + Eur/(,3) :59‘,“ .é — “/33 . ea (c) cw) = me{<3’+ j3fi)ej2”:3)‘} ( £4; (1/?) = E L 0"" ' W:a (d) xd(t) = 12 cos(27r(23)t + 7r/3) For each of the following signals, pick one of the representations above that defines an identical signal. Write your answer ((a),(b),(c),(d)) in the box next to each signal. 3ejvr/3e—j467rt + 3e‘j7r/Bej467rt : 6603(4c‘fl é ~ 11/33 + 21 mew/sewn} : u a; (Law 3 ”commas/3) : (3 “Sc/(fie «“42, V %{12e‘j"/3e"2"(23”} : /3w5(4éné'“/3> 6cos(27r(23)t—7r/3) = £005 (1/4le ‘ “1/3) “eh/3mm+8‘j"/36"'46“) 3 5 0°; (1/4111! ”L Tré) ’2' Problem su-OI—Q.1 .2: 2/ , Define a:(t) as . x(t) = 2\/§cos(2.57rt -— 37r/4) + 4cos(2.57r(t + 5)) (a) Express m(t) in the form a:(t) = Acos(w0t + ¢) by finding the numerical values of A, 45, and tag (give the correct units). 3 3 n /L/ X.‘ QJSQ‘) :DJS((,05(—3fl/q)+- g,\fl[3n/,,)> A: (91/3 ’4 <15: I3 5w fr/ W4C =’/¢J 2 4(cos[%)*g)$”’ (3)) we: 3 5.“. ”(1/5 (b) Make two complex plane plots to illustrate how complex amplitudes (phasors) where used ’ to solve part (a). On the first plot, show the two complex amplitudes that are to be added; on the second plot, show your solution as a vector and the addition of the two complex amplitudes as vectors (head-to—tail). :15 (a) The incomplete spectra for two real signals 2:1(t) and x2(t) are shown in the following figures. Fill in the empty boxes for the missing components. , ,I’ , 3W3 -- y 8e‘17r/2' »r n / x1(t) 3e—j51r/6 ”A‘) W I 1 4ej31r/4 55 f (H2) —55 ~35 -—12.5 3 12.5 5 x2(t) 483.174 1 I 1 4e”j"'/4 f (HZ) —35 -—12.5 E 12.5 35 (b) Write an equation for x2(t) in terms of cosine functions X;(£)= '71" L; 403 (903 5311'?" ‘3 4- 8605 (3(3$)nt5)> TV )((6\ 7‘ 74 Does (951'5’ /3+8w$(70fl£ /‘/> A . Problem su—Ol-Q.1.3: (c) Draw the spectrum representation for $3.05) = :51 (t) + m2(t). ma) vs’r ,3 5' -IA.( 0 “or 35' ff 4(LOS(*’/)*J “'\("5"/’/j)’q<"a'+~l “)'.Jfi+ Uh”) z-fl’in‘ffz “bf/rm) 1”) q(1f§, )5»- ;_J—.5;.,13 ,4 (sf/'9’ Ll(¢»93("l*J“\‘[ (d)stt= t+ t erid?Ifso,whatsthef d tlfe 7 3() m1() x2()p cm 1 un amena rquency. Q 5H1 ‘n/ #03; W»: films 61A,,émuxd ‘4'7'9‘7 0! all o/Ivu, Afimwcs m Ina/6,910; 04 9.3"”: (MC/h: 54. S's/7,2, 3;;fi) V "3 Problem su—Ol-Q.1.4: . 2 Define a:(t) as :v(t) = 20 + 60 cos((27r/15)t — 27r/3) (a) What is the fundamental period T0 of x(t)? W: I“" z '3» -—’-—- 1/ o Qfl/figgb35, filfin'}. -- (b) What is the time shift tm of z(t)? ¢=-_a_§r_r_,:_w ,., ). gm: 7?.(~£[email protected] (0) Draw a detailed plot of 53(t) over the domain |t| S gTo. Label carefully and include the amplitude, tm, and To. ””73; z ALI». r 4 4 3;. r) ((1) Define y(t) = $05 —— to). Find to so that the signal y(t) has its maximum value at t = 0. There . are an infinite number of tos, so give the general form. K ¢: 0 ; r D“, d! ylé) = am “has (3nfl§(t~r-i;§-i§ ...
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