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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING QUIZ #3 DATE: 1Apr05 COURSE: ECE2025 NAME: GT #: LAST, FIRST (ex: gtz123q ) 3 points 3 points 3 points Recitation Section: Circle the date & time when your Recitation Section meets (not Lab): L05:TuesNoon (Chang) L06:ThurNoon (Ingram) L07:Tues1:30pm (Chang) L08:Thurs1:30pm (Zhou) L01:M3pm (Williams) L09:Tues3pm (Casinovi) L02:W3pm (Juang) L10:Thur3pm (Zhou) L03:M4:30pm (Casinovi) L11:Tues4:30pm (Casinovi) L04:W4:30pm (Juang) GTSav: (Moore) • 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 HANDWRITTEN 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 No Rec 3 PROBLEM sp05Q.3.1: (a) Determine the frequency response of the FIR system: y [ n ] = 10 x [ n 2] 10 x [ n 5] Give your answer as a formula in the following form: H ( e j ˆ ω ) = je j α ˆ ω β sin (λ ˆ ω) by finding numerical values for α , β and λ . α = β = λ = (b) For the system in part (a), determine the output signal y [ n ] when the input signal is x [ n ] = √ 7 + 100 cos ( . 1 π n ) (c) Write a few lines of MATLAB code that would compute the specific values of the frequency response needed in part (b). PROBLEM sp05Q.3.2: The diagram in Fig. 1 depicts a cascade connection of two linear timeinvariant systems, i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system. LTI System #1 H 1 ( z ) LTI System #2 H 2 ( z ) x [ n ] v [ n ] y [ n ] System #1 is an IIR filter described by the system function: H 1 ( z ) = z 2 10 z 3 1 . 9 z 1 (a) Determine the impulse response sequence, h 1 [ n ], of the first system. Give your answer as a plot. 6 3 2 1 1 2 3 4 5 n Label Carefully (b) Determine the difference equation of the second system so that the following condition is true: When the input is a shifted impulse , x [ n ] = δ [ n 1], the output is another shifted impulse, y [ n ] = δ [ n 3]....
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This note was uploaded on 02/07/2012 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Tech.
 Spring '08
 JUANG

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