ENEE241hw09

ENEE241hw09 - ENEE 241 02 * HOMEWORK ASSIGNMENT 9 Due Tue...

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Unformatted text preview: ENEE 241 02 * HOMEWORK ASSIGNMENT 9 Due Tue 04/12 Problem 9A The signal x = a b c 0 0 0 a b c 0 0 0 T has DFT X given by X = D D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 T (i) (4 pts.) For which indices k is D k necessarily equal to zero? (ii) (4 pts.) If x (1) = a b c T , express the DFT X (1) in terms of nonzero D k s. (iii) (4 pts.) If x (2) = a b c a b c a b c T , express the DFT X (2) in terms of nonzero D k s. (iv) (4 pts.) x (3) = a jb- c 0 0 0- a- jb c 0 0 0 T has DFT X (3) given by X (3) = E E 1 E 2 E 3 E 4 E 5 E 6 E 7 E 8 E 9 E 10 E 11 T express each E in terms of nonzero D k s. (v) (4 pts.) If the time-domain signal x (4) has DFT X (4) = 0 0 0 a b c T , express the entries of x (4) in terms of nonzero D k s. Problem 9B The data set data09.txt contains fifty-six noisy samples of a continuous-time signal which is a sum of two sinusoids at frequencies f 1 and f 2 (Hz), i.e., s ( t ) = A 1 cos(2 f 1 t + 1 ) + A 2 cos(2 f 2 t + 2 ) The sampling rate f s equals 700 samples/second (i.e., the fifty-six samples correspond to exactlyequals 700 samples/second (i....
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ENEE241hw09 - ENEE 241 02 * HOMEWORK ASSIGNMENT 9 Due Tue...

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