HW13f08 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Fall 2008 Problem Set #13 Assigned: 17-Nov-08 Due Date: Week of 1-Dec-08 Reading: In SP First , Chapters 11 and 12 on Fourier Transform and its Applications . Please check t-square.gatech.edu often. All official course announcements are posted there. ALL of the STARRED problems should be turned in for grading. A solution will be posted to the web. Some problems have solutions similar to those found on the CD-ROM. Your homework is due in recitation at the beginning of class. After the beginning of your assigned recitation time, the homework is considered late and will be given a zero. Please follow the format guidelines (cover page, etc.) for homework. All students should turn this in on Wednesday 12/3 or Thursday 12/4; this will be during recitation or lab, depending on your particular schedule. PROBLEM 13.1 *: (a) Determine the forward Fourier Transform X ( ), given x ( t ): (i) x ( t ) = 3 cos 2 (17 t ) (ii) x ( t ) = δ ( t + 1) - 2 e - t u ( t - 1) (iii) x ( t ) = d dt ± sin(17 π ( t - 2)) 2 πt - 4 π ² (iv) x ( t ) = u ( t - 1) - u ( t - 8) (v) x ( t ) = 7 + 10 cos(4 t - π/ 3) (b) Determine the inverse Fourier Transform x ( t ), given X ( ): (i) X ( ) = cos 2 (3 ω ) (ii) X ( ) = - 1 2 + (iii) X ( ) = j 13 { δ ( ω - 3 π ) - δ ( ω + 3 π ) } (iv) X ( ) = u ( ω + π ) u ( π - ω ) e - jω/ 10 (v) X ( ) = 1 1 + j ( ω - 1) + 1 1 + j ( ω + 1)
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PROBLEM 13.2 *: The impulse response of an LTI system is given by
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HW13f08 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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