(a) An LTI system is described by the following differential equation:

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(a) An LTI system is described by the following differential equation: (10 points) d2y(t) dt2 + 2dy(t)dt − 8y(t) = 3x(t) Use Laplace Transform to find the Transfer Function, H(s). (b) Assume the transfer function H(z) of the system is given by the following transfer function: (10 points) H(z) = 3 s2+2s−8 Determine the Impulse Response, h(t), which is the inverse Laplace Transform of the transfer function H(z). You might use the attached Laplace Transform Table.

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(a) An LTI system is described by the following differential equation: (10 points)

\frac{d^{2} y (t)}{d t^{2}} + 2 \frac{d y (t)}{d t} - 8 y (t) = 3 x (t)

Use Laplace Transform to find the Transfer Function,

H (s)

.

(b) Assume the transfer function $H (z)$ of the system is given by the following transfer function: (10 points)

H (z) = \frac{3}{s^{2} + 2 s - 8}

Determine the Impulse Response,

h (t)

, which is the inverse Laplace Transform of the transfer function

H (z)

. You might use the attached Laplace Transform Table.

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