Exam+_3_v2_ans

# Exam+_3_v2_ans - EEL 3112 Exam#3 Spring 2014 Name_ANSWERS...

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EEL 3112 Exam #3, Spring 2014 Name: ____ANSWERS________________________________ ID: _______________________________________ Instructions: Complete the quiz in the space provided. When time is called, stop all work and follow the instructions provided. Any work that is not collected when called for will not be graded. The honor system will be strictly enforced. Allowed Open book Open notes Calculators (including laptops) Laptops access to the Internet limited to Sakai. Disallowed No cell phone use or text messaging. Topical Coverage: Fourier series and transform (Lessons 24-33) Quiz basis: 100 points TURN YOUR CELL PHONE OFF!!!!!! _________________________________ 1

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EEL 3112 Exam #3, Spring 2014 Q1. Fourier Series Assume that the  (amplitude) periodic square wave, shown in Figure above, has a trigonometric CTFS representation given by: a) What is the signal’s fundamental frequency 0 in r/s? [5] The period of x(t) is T 0 = 2 . Therefore f 0 =1/2 and 0 = 1 r/s. b) What is the compact Fourier series ( ) representation of x(t)? That is, what are the values of C 0 , C n and n ? [10] The compact Fourier series has the form: Substituting A 0 =A n =0, C n =B n (n odd), 0 otherwise. Therefore: Assume that the trigonometric Fourier Series representation of x(t) continues to be: c) What is the signal’s DC value? [5] Use the fact that x(t) has odd symmetry or A 0 =0.
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