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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2008 Problem Set #3 Assigned: Week of 2Jun08 Due Date: 10/11Jun08 Special due dates: Tuesday recitations will turn this in at the start of their recitation as usual. Monday recitations can turn this in at the start of their Wednesday lab. This is to give a bit of a buffer to adapt for the quiz timing; I realize people didn’t really get a chance to start this homework early because of the quiz, and people in Monday recitations will have difficulty getting inperson help over the weekend. Warning: This is one of the most challenging homeworks of the semester. Do not leave this one until the last minute! Start early! If you can make it through this homework, you can survive anything else we’ll throw at you in ECE2025. First quiz is in class on Friday, 6Jun08, in lecture. Remember there are no makeup exams; if you have a valid, documented excuse for missing the exam, your Quiz #2 score will count for your Quiz #1 score. Oversleeping is not a valid excuse. Note that Quiz #1 won’t cover the Fourier series material; however, the kinds of manipulations you need to do in parts (a) and (c) of Problem 3.1 will incidentally provide some good practice for Quiz #1. Please check the WebCT “Bulletin Board” daily. All official course announcements will be posted there. ALL of the STARRED problems should be turned in for grading. After this assignment is handed in by everyone, a solution to all the starred problems will be posted to the web. PROBLEM 3.1 *: (10 pts) Which of the following signals are periodic? For those that are periodic, find the fundamental frequency in radians per second, ω , and the nonzero F.S. (Fourier Series) coefficients a k for all k . (Important: you should be able to do this problem without actually having to compute any integrals! While working the problem, stop yourself the moment you write an integral sign and spend some time thinking. You can generally rewrite the expressions using Euler’s formula and expand things out.) (a) x ( t ) = 30cos(120 πt + π/ 5)cos(40 πt − π/ 4) (b) x ( t ) = cos(5 πt − 3 π/ 5) + cos( √ 17 · 5 πt − 2 π/ 7) (c) x ( t ) = − 5 + 8sin(8 . 4 πt + 5 π/ 9) − 24cos(8 . 6 πt + 3 π/ 4) (d) x ( t ) is given by the infinite sum x ( t ) = ∞ summationdisplay k =∞  k   k  3 + 7 e j 120 πkt (Hint: Don’t let the decimal points disturb you – part (c) is periodic!) PROBLEM 3.2PROBLEM 3....
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 Spring '08
 JUANG
 Fourier Series, Signal Processing, F.S. coeﬃcients, xBP

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