Consider the discrete time system y(n) ay(n 1) (1 0) x (n) n 0 where a 0 9 an dy ( 1) 0 (a) Compute and sketch the output y1(n) of the system to the input signals x1(n) sin2f1n 0n100, where f1 f2 1 5, f3 1 10, f4 1 20 (b) Compute and sketch the magnitude and phase response of the system and use these results to explain the response of the system to the signals given in part (a)

Question: Consider the discrete-time system y(n) = ay(n 1) + (1 0) x (n) n 0 where a = 0.9 an dy (-1) =

Consider the discrete-time system y(n) = ay(n – 1) + (1 – 0) x (n) n ≥ 0 where a = 0.9 an dy (-1) = 0.
(a) Compute and sketch the output y1(n) of the system to the input signals x1(n) = sin2πf1n 0≤n≤100, where f1 = ¼. f2 = 1/5, f3 = 1/10, f4 = 1/20
(b) Compute and sketch the magnitude and phase response of the system and use these results to explain the response of the system to the signals given in part (a).

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