Suppose we are given the following information about a causal and stable LTI systemS

Chapter 9, Problem 9.34

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Suppose we are given the following information about a causal and stable LTI systemS with impulse response h(t) and a rational system function H(s): 1. H(l) = 0.2. 2. When the input is u(t), the output is absolutely integrable. 3. When the input is tu(t), the output is not absolutely integrable. 4. The signal d2h(t)ldt2 + 2 dh(t)ldt + 2h(t) is of finite duration. 5. H(s) has exactly one zero at infinity. Determine H (s) and its region of convergence.

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