hw18 - ENEE 241 02* HOMEWORK ASSIGNMENT 18 Due Tue 04/28...

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Unformatted text preview: ENEE 241 02* HOMEWORK ASSIGNMENT 18 Due Tue 04/28 (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 . 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 linear combination of two symmetric rectangular pulse trains plus a constant. 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 ).-8 -7 -5 -4 -3 -1 0 1 3 4 5 7 8 t s ( t ) 2 ... ... 1 (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; S k , k 6 = 0. For (iv)(vi), consider the periodic signal y ( t ) shown below....
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hw18 - ENEE 241 02* HOMEWORK ASSIGNMENT 18 Due Tue 04/28...

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