# hw03 - ENEE 241 02 HOMEWORK ASSIGNMENT 3 Due Thu 02/12 3 2...

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ENEE 241 02* HOMEWORK ASSIGNMENT 3 Due Thu 02/12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -3 -2 -1 0 1 2 3 Two periods of the sinusoid x ( t ) = A cos(Ω t + φ ) are plotted above. The value of x (0) equals - 3sin( π/ 5). (i) (6 pts.) Determine A , Ω and φ . Express φ as an exact rational multiple of π in the range [0 , 2 π ). In what follows: A and φ are as found in part (i) and x [ n ] = x ( nT s ), where T s is a suitably chosen sampling period. (ii) (3 pts.) For what values of T s is it true that x [ n ] is constant in n ? (iii) (3 pts.) For what values of T s is it true that x [ n ] = - x [ n - 1] for all n ? (iv) (4 pts.) Determine all values of T s such that x [ n ] = A cos((5 π/ 8) n + φ ). (v) (4 pts.) Determine all values of T s such that x [ n ] = A cos(( π/ 6) n - φ ). Solved Examples S 3.1 ( P 1.19 in textbook). The continuous-time sinusoid x ( t ) = cos(150 πt + φ ) is sampled every T s = 3 . 0 ms starting at t = 0. The resulting discrete-time sinusoid is x [ n ] = x ( nT s ) (i)

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hw03 - ENEE 241 02 HOMEWORK ASSIGNMENT 3 Due Thu 02/12 3 2...

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