The system function H(z) of a causal linear time invariant system has the pole zero configuration shown in Figure, 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 u n 1 (ii) The sequence x n obtained from sampling the continuous time signal x(t) 50 10 cos 20t 30 cos 40t at a sampling frequency s 2(40) rad s Im z plane Double zero Re 2 wi

Question: The system function H(z) of a causal linear time-invariant system has the pole-zero configuration shown in Figure, It is also known that H(z) = 6

The system function H(z) of a causal linear time-invariant system has the pole-zero configuration shown in Figure, It is also known that H(z) = 6 when z = 1.

Im z-plane Double zero Re 2 wi-

(a) Determine H(z).

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

(i) x[n] = u[n] – ½ 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 Ω_s = 2π(40) rad/s

Im z-plane Double zero Re 2 wi-

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