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**Unformatted text preview: **GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING QUIZ #1 DATE: 6-Feb-09 COURSE: ECE-2025 NAME: GT username: LAST, FIRST (ex: gtbuzz7 ) 3 points 3 points 3 points Recitation Section: Circle the date & time when your Recitation Section meets (not Lab): L05:Tues-Noon (Bhatti) L06:Thur-Noon (Barry) L07:Tues-1:30pm (Bhatti) L08:Thur-1:30pm (Barry) L01:M-3pm (Chang) L09:Tues-3pm (Lee) L02:W-3pm (Fekri) L11:Tues-4:30pm (Lee) L04:W-4:30pm (Fekri) Write your name on the front page ONLY. DO NOT unstaple the test. Closed book, but a calculator is permitted. One page ( 8 1 2 00 11 00 ) of HAND-WRITTEN notes permitted. OK to write on both sides. JUSTIFY your reasoning clearly to receive partial credit. Explanations are also REQUIRED to receive FULL credit for any answer. 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 previous pages. Problem Value Score 1 40 2 30 3 30 No/Wrong Rec 3 PROBLEM SPR-09-Q.1.1: (a) The signal plotted below is the sum of two sinusoids; determine the amplitudes and phases, as well as the frequencies in rad/s.-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 5 6 7 8 Time t (sec) A 1 D 1 D ! 1 D rad/s A 2 D 2 D ! 2 D rad/s (b) Express this signal as a sinusoid in standard form, i.e., A cos .! t C '/ . s a .t/ D 150e j =4 e j2200 t C 150e j =4 e j2200 t (c) Express this signal as a sinusoid in standard form, i.e., A cos .! t C '/ . s b .t/ D < e n . 1 C j6/e j4t o PROBLEM SPR-09-Q.1.2: The following MATLAB code defines a periodic signal as the sum of sinusoids: tt = -10:0.00001:10; %- in seconds xxt = cos(1.2*tt)); kk=2; xxt = xxt + kk*pi*cos(1.5*kk*tt + kk*2*pi/3); kk=4; xxt = xxt + real( (-4+3i)*exp(j*1.8*kk*tt) ); In the following questions, the signal x.t/ corresponds to the MATLAB vector xxt ....

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