quiz1a_su10_soln

quiz1a_su10_soln - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL...

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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL 3:: COMPUTER ENGINEERING QUIZ #1 DATE: 11-JUN—10 COURSE: ECE 2025 NAME: STUDENT #: LAST, FIRST Recitation Section(2 points): Circle the day 85 time when your Recitation Section meets: L01: M 2:40-4:25 (Taylor) L03: T 10—11345 (Hunt) L05: T 2—3345 (Romberg) L02: M 4:406:25 (Taylor) L04: T 1200—1315 (Hunt) L06: T 4-5315 (Romberg) 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- 9 Unless stated otherwise, JUSTIFY your reasoning clearly to receive any partial credit. Explanations are also required to receive full credit for any answer. 0 You must write your answer in the space pr0vided 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 previous pages. 1 32 2 33 - - - we Problem 01.1: Each part of this problem is independent of the others. (a) (8 points) Find TWO values of 9 satisfying —7r < 6 5 1r such that Re{(2 + flew} = 0. 91: I'lozn‘ 92:;7-‘9345/ J .‘2‘63GJ = 21531 6 '1‘ “faded— b3» %- .4é3é 0"” -(TT/zqt.’*~r‘£-3é) (b) (8 points) Plot the complex vector (1 + 3%”. o'lt_ ‘(1I)Mbdq ‘ “J: :01 .“9 W513: 3-I (c) (8 points) Make a. plot of |e(—1+j2"}‘| over 0 S t g 1. [Be sure to notice the magnitude bars!) \’\.: Ie‘t ‘16“an W W54) 6“" 1— (d) (8 points) If 5.6 exp(0.312j) = find a and b. a:geaf’b:.4%% a”, 4+5?“ _ 1.043) 3 aec‘wm'“ rJCfiWU Problem Q12: Each part of this problem is independent of the others. (a) (8 points) Express 3 cos(wt + a) + 3 cos (wt + 16) as A cos(wt + 95), where A and gt are functions MW (55) 4 e: ‘3 1 COW“ W) C Wig if Eff't 'ZQfiffij (b) (8 points) Simplify the following expression: 1 xmemiamm_5tmtj k=0 You should be able to do this without doing any explicit calculations! Sketch ated with the terms, and give an intuitive explanation for our answer. (194:. phasors assoii - m XS“ (’6 4"“ W“ t ” d A 5.592158 C (3%“!133- $531- 53” 57 F J ‘I --«« 2'- Wfi%£wm sg~mu gm?fe .1 f .. IA a? II/,...—:. (i) (9 points) Plot the two-sided spectrum of 55(t) 0n the graph on the next page. Be sure to label all components of the spectrum with their frequency (in radians/sec) and their Complex amplitude. (092(046)9V: (- ‘ v f db .Jdé ‘ J c Edi-+5”! X67 +6? )(Cfljigj MT L " 2; 'u- Jute Mi", 4% sew” rt: M c J frequency in rad / sec (ii) (8 points) Find its fundamantal frequency in Hz. 1% = /2 n fl: Mai, ‘ *3” "1967 “ML? 5'3 W [9%) 5% W???“ C. “3: /§* Problem Q13: (3) Over the interval 0 < t < 1, y(t) has instantaneous frequency fmfi) = 200.9(27r2t) in Hz. (i) (8 points) Sketch fyifi) in the space below {113+ 96% ’ m w / 5- Jit’k-jaucix (jib “mam-«5) azfl’ AA: gnu-— 5? r? m" 371""; z/p'f @§{4fi%)§6f 3; + 4-? :2”? t. 14 a u-r + 5%47Ff #4- (b) A real signal :50) = Acos(1501rt+ 95) + Bcos(w1(t — 7)) + CCUSfidgt) + D has the following twosided spectrum: 53—3517,” 5 563‘an — 100 —75 ~50 0 50 75 100 f frequency in Hz (i) (8 points) Determine A, B, C, D, L01, Leg, (,5, and 7' the signal $(t) with the above spec- trum. EL "Dr:- Dc: 3 B=m/_’_‘~3___ {ML like C=__:.;“l' _ “an wit: 1?? T Q D=mfifl_ fieiwvhwkf be _ 5’3"”?- cfm-fanwt’f'lz r $‘ final GI: _. L} '2? 1:— “1” "2—: my w W ’1 if “i “7‘ R " . w2 =£.:___r_9 '3 «5 'L .... U; T:_ {6:35:38} (ii) (8 points) Is the signal 3:09) is periodic? If so, determine the fundamental frequency f0, of the signal f0 ‘3" ...
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This note was uploaded on 10/21/2010 for the course ECE 2025 taught by Professor Juang during the Summer '08 term at Georgia Tech.

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quiz1a_su10_soln - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL...

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