An ltic system has an impulse response ht with the laplace

Question

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.