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 π t + 2 . 3) + 1 . 4 cos(330 π t - 0 . 4) + 6 . 2 cos(440 π t + 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 coe ffi cient S k (it su ffi ces 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 Fourier 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 ) over its first period [0 , T 0 ). Submit the commands used and the resulting plot; do not include a printout of the vector. Solved Examples S 10.1 Determine the fundamental period T 0 of s ( t ) = 8 cos(46 π t ) cos(50 π t ) cos(60 π t ) S 10.2 If s ( t ) = 11 + cos(30 π t ) - 5 sin(37 . 5 π t ) - 9 cos(52 . 5 π t ) + 2 sin(52 . 5 π t ) ,

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