ENEE241hw11

# ENEE241hw11 - ENEE 241 02 HOMEWORK ASSIGNMENT 11 Due Thu...

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Unformatted text preview: ENEE 241 02* HOMEWORK ASSIGNMENT 11 Due Thu 04/25 Problem 11A (i) (2 pts.) In the lecture notes, you will find the Fourier series for the symmetric (even) rectangular pulse train of unit height and duty factor α . Write down both the complex and real (cosines-only) form of the series for a fundamental period T = 8. (ii) (5 pts.) Express the periodic signal s ( t ) (of period T = 8) shown below as a sum of three symmetric rectangular pulse trains of the same period. Using the result of (i), derive the complex Fourier series coefficients { S k } . Also, write down the real (cosines-only) form of the series for s ( t ). s ( t ) 1 ... ...-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 t (iii) (3 pts.) Sketch the periodic signal x ( t ) which has period T = 8 (i.e., same as s ( t )) and complex Fourier series coefficients given by X k = , k = 0; 2 S k , k = 0. For (iv)–(vi), consider the periodic signal y ( t ) shown below....
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ENEE241hw11 - ENEE 241 02 HOMEWORK ASSIGNMENT 11 Due Thu...

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