Question 4 Marks: 30 (a) Consider a causal continues-time system characterized by the following differential equation: d?y(t) dy(t) + 16 dt + 24y(t) = 2x(t) dt2 Where x(t) is the input and y(t) is the output of the system. Apply Laplace transform properties to obtain the following: [15 Marks] [5 Marks] (1) The system response H(s). (ii) The poles and zeros of H(s). (b) A discrete time signal x[n] is given by: () u[n] 8. n x[n] = 3"u[n] + Apply z-transform properties to determine the z-transform of the signal x[n] and its region [10 Marks] of convergence.

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Question 4
Marks: 30
(a) Consider a causal continues-time system characterized by the following differential
equation:
d?y(t)
dy(t)
+ 16
+24y(t) = 2x(t)
dt2
dt
Where x(t) is the input and y(t) is the output of the system. Apply Laplace transform
properties to obtain the following:
(1) The system response H(s).
[15 Marks]
(ii) The poles and zeros of H(s).
[5 Marks]
(b) A discrete time signal x[n] is given by:
x[n] = 3"u[n] +
*u[n]
8.
Apply z-transform properties to determine the z-transform of the signal x[n] and its region
[10 Marks]
of convergence.
Transcribed Image Text:Question 4 Marks: 30 (a) Consider a causal continues-time system characterized by the following differential equation: d?y(t) dy(t) + 16 +24y(t) = 2x(t) dt2 dt Where x(t) is the input and y(t) is the output of the system. Apply Laplace transform properties to obtain the following: (1) The system response H(s). [15 Marks] (ii) The poles and zeros of H(s). [5 Marks] (b) A discrete time signal x[n] is given by: x[n] = 3"u[n] + *u[n] 8. Apply z-transform properties to determine the z-transform of the signal x[n] and its region [10 Marks] of convergence.
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