: Laplace and Z-Transforms Properties

Consider a linear time invariant (LTI) system of Figure Q2. Given that the input of the system X(s) is a unit step function and the output Y(s) of the system is described by the following expression:

Figure Q2

Determine the following characteristics of the LTI system:

• The transfer function H(s). [4 Marks]
• The output response y(t) for an input signal x(t) = 5t u(t).[8 Marks]
• The inverse Laplace transforms of [8 Marks]

Consider the causal continues-time LTI system characterized by the following differential equation

(i)Use Laplace transform method to determine the poles, zeroes, region of the convergence (ROC) and the output response y(t) of the system.[14 Marks]

• Sketch the pole-zero pattern of and its ROC.[6 Marks]