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).