The system function H(z) of a causal LTI system has the pole–zero configuration shown in...

The system function H(z) of a causal LTI system has the pole–zero configuration shown in Figure P5.48. It is also known that H(z) = 6 when z = 1.

(a) Determine H(z).

(b) Determine the impulse response h[n] of the system.

(c) Determine the response of the system to the following input signals:

(i) x[n] = u[n] − 12 u[n − 1]

(ii) The sequence x[n] obtained from sampling the continuous-time signal x(t) = 50 + 10 cos 20πt + 30 cos 40πt at a sampling frequency Ωs = 2π(40) rad/s.