The input-output relationship of a continuous-time, causal LTI system is given by the differential equation below....

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The input-output relationship of a continuous-time, causal LTI system is given by the differential equation below. dx(t) dy(t) + 2y(t) = x(t) + dt dt Find the transfer function H (s) and the corresponding region of convergence (ROC) for this system. Plot the s-domain pole-zero plot and the ROC. a) b) Find the impulse response h(t) for this system. Is this system stable? Explain. c) Calculate the output signal y(t) for input signal x(t) = e-atu(t), with a = 5 (use Laplace transform). Clearly plot the ROC for the transfer function H(s) if the impulse response of the system was anti-causal (non-causal). (do not calculate the impulse response, just plot the ROC). d) The input-output relationship of a continuous-time, causal LTI system is given by the differential equation below. dx(t) dy(t) + 2y(t) = x(t) + dt dt Find the transfer function H (s) and the corresponding region of convergence (ROC) for this system. Plot the s-domain pole-zero plot and the ROC. a) b) Find the impulse response h(t) for this system. Is this system stable? Explain. c) Calculate the output signal y(t) for input signal x(t) = e-atu(t), with a = 5 (use Laplace transform). Clearly plot the ROC for the transfer function H(s) if the impulse response of the system was anti-causal (non-causal). (do not calculate the impulse response, just plot the ROC). d)