Problem 4 [6 points] (Laplace transform) A linear time-invariant (LTI) system has input x(t), impulse response h(t), and

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Problem 4 6 Points Laplace Transform A Linear Time Invariant Lti System Has Input X T Impulse Response H T And 1 (52.24 KiB) Viewed 18 times

Problem 4 [6 points] (Laplace transform) A linear time-invariant (LTI) system has input x(t), impulse response h(t), and output y(t). Assume that the input is given by: x(t) = e¹u(-t) where u(t) is the unit step function. Regarding the impulse response, we know that h(t) is causal and BIBO stable, and its Laplace transform is given by: -8 H(s) = 8+5 i) [2 points] Calculate the Laplace transform X(s) and its region of convergence (ROC). ii) [2 points] Determine the ROC of H(s) and calculate h(t). iii) [1 point] Calculate Y(s) and its ROC. iv) [1 point] Calculate y(t). Note: You can use the properties of the Laplace transform and transformation pairs listed in the Tables 9.1 and 9.2 of the book.