# hw13 - ENEE 241 02 HOMEWORK ASSIGNMENT 13 Due Tue 04/07...

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ENEE 241 02* HOMEWORK ASSIGNMENT 13 Due Tue 04/07 Problem 13A The real-valued signal vector s has DFT S = £ 12 z 1 - 2 j z 2 4 - j z 3 3 + 2 j z 4 - 2 - 5 j / T (i) (2 pts.) What are the values of z 1 , z 2 , z 3 and z 4 ? (ii) (3 pts.) Without using complex algebra (or MATLAB), determine the sum of the entries of s . (iii) (4 pts.) Display the amplitude ( | S [ k ] | ) and phase ( S [ k ]) spectra as vectors. (iv) (7 pts.) Write an equation for s [ n ] (where n = 0 : 8) in the form of a constant plus three real-valued sinusoids with frequencies between 0 and π . (v) (4 pts.) In MATLAB, generate the vector s given by the equation found in part (iv) and verify that fft(s) agrees with S . Problem 13B The signal vector s is given by s = £ a b c d e f g h / T (i) (8 pts.) Display the following vectors: s (1) = s - Rs s (2) = P 2 s + P - 2 s s (3) = F 4 Rs s (4) = Fs + F - 1 s (ii) (12 pts.) Express the following vectors in terms of P , R , F and s : s (5) = £ 2 a b + h c

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hw13 - ENEE 241 02 HOMEWORK ASSIGNMENT 13 Due Tue 04/07...

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