ENEE241hw10

ENEE241hw10 - ENEE 241 02 HOMEWORK ASSIGNMENT 10 Due Tue...

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ENEE 241 02* HOMEWORK ASSIGNMENT 10 Due Tue 04/19 Let s ( t )= - 9 . 1+3 . 8 cos(165 πt +2 . 3) + 1 . 4 cos(330 πt - 0 . 4) + 6 . 2 cos(440 πt +1 . 8) , where t is in seconds. (i) (4 pts.) Is s ( t ) periodic? If so, what is its fundamental period T 0 and angular frequency Ω 0 ? (ii) (6 pts.) If s ( t )= ± k = -∞ S k e jk Ω 0 t , determine the value of each coeFcient S k (it suFces to leave it in polar form). (iii) (4 pts.) Suppose that s ( t ) is sampled every T s = T 0 /N seconds, where N is an integer, to produce s [ n ]= s ( nT s ) Write an equation for s [ n ] in terms of real sinusoids. What are the frequencies of these sinusoids? Are they ±ourier frequencies for an N -point vector? (iv) (6 pts.) Let N = 300. Use the IFFT function in MATLAB to generate the vector s [0 : 299], which consists of N uniform samples of s ( t )overits²rstper iod[0 ,T 0 ). Submit the commands used and the resulting plot; do not include a printout of the vector.
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This note was uploaded on 09/27/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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ENEE241hw10 - ENEE 241 02 HOMEWORK ASSIGNMENT 10 Due Tue...

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