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**Unformatted text preview: **GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 7-Dec-04 COURSE: ECE-2025 NAME: GT # LAST, FIRST (e.g. gtg123a) Recitation Section: Circle the date & time when your Recitation Section meets (not Lab): L02:Thurs-9:30 (Anderson) L03:Tues-Noon (Williams) L05:Tues-1:30 (Williams) L06:Thurs-1:30 (Anderson) L07:Tues-3:00 (Durey) L08:Thurs-3:00 (Smith) L09:Tues-4:30 (Durey) L10:Thurs-4:30 (Smith) L13:Mon-3:00 (McClellan) L14:Wed-3:00 (Taylor) L15:Mon-4:30 (Hayes) L16:Wed-4:30 (Taylor) 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 25 2 25 3 25 4 25 5 25 6 25 7 25 8 25 PROBLEM fall-04-F.1: In each of the following cases, simplify the expression as much as possible. (a) cos(3 / 4 t- / 2) ( t- 3) = (b) [( t + 1) u ( t + 1)] * ( t- 2) = (c) Z 2 e- 10 ( - 3) d = (d) x [ n ] = 5cos(0 . 3 n + / 2) + 5 2cos(0 . 3 n- / 4) = PROBLEM fall-04-F.2:-- Continuous-Time LTI System h ( t ) and H ( j ) x ( t ) y ( t ) The periodic input to the above LTI system has the Fourier transform X ( j ) drawn below:-5 -4 -2 - 2 4 5 -3 3 X ( j ) (2 / 5 ) (2 / ) (2 / 2) (2 / ) (2 / 5 ) (-2 / 3 ) (-2 / 3 ) where the dark arrows denote impulses. For the following outputs of the system, determine fromwhere the dark arrows denote impulses....

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