Question

Problem 4 (15 marks) A causal LTI system has impulse response \begin{equation} h(t) = e^{-t} + \sin t, \quad t \ge 0 \end{equation} Compute the output response when the input is the function $x(t) = e^{-t}u(t)$.

          Problem 4 (15 marks) A causal LTI system has impulse response \begin{equation*} h(t) = e^{-t} + \sin t, \quad t \ge 0 \end{equation*} Compute the output response when the input is the function $x(t) = e^{-t}u(t)$.

Problem 4 (15 marks) A causal LTI system has impulse response
h(t) = e^-t + sin t, t ≥ 0
Compute the output response when the input is the function x(t) = e^-tu(t).

Added by John G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sahil Kumar

Step 1

The Laplace transform of e^(-t) is 1/(s+1) and the Laplace transform of sin(t) is (s)/(s^2+1). Therefore, the Laplace transform of h(t) is H(s) = 1/(s+1) + (s)/(s^2+1). Show more…

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A causal LTI system has impulse response h(t) = e^(-t) + sin(t), t â‰¥ 0. Compute the output response when the input is the function x(t) = e^(-t)u(t).