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Question: An LTIC system has an impulse response h(t) with the Laplace transfer function H(s), which satisfies the following properties:
(a) the impulse response h(t) is even and real-valued;
(b) the area enclosed by the impulse response is 8, i.e
(c) the Laplace transfer function H(s) has four poles but no zeros;
(d) the Laplace transfer function H(s) has a complex pole at s = 0.5 exp(jπ/4).
Determine the Laplace transfer function H(s) and the associated ROC.
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