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Consider an LTI system with input x(t) = e-t u(t) and impulse response h(t) = e-2t u(t)

Chapter 9, Problem 9.29

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QUESTION:

Consider an LTI system with input x(t) = e-t u(t) and impulse response h(t) = e-2t u(t). (a) Determine the Laplace transforms of x(t) and h(t). (b) Using the convolution property, determine the Laplace transform Y(s) of the output y(t). (c) From the Laplace transform of y(t) as obtained in part (b), determine y(t). (d) Verify your result in part (c) by explicitly convolving x(t) and h(t).

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QUESTION:

Consider an LTI system with input x(t) = e-t u(t) and impulse response h(t) = e-2t u(t). (a) Determine the Laplace transforms of x(t) and h(t). (b) Using the convolution property, determine the Laplace transform Y(s) of the output y(t). (c) From the Laplace transform of y(t) as obtained in part (b), determine y(t). (d) Verify your result in part (c) by explicitly convolving x(t) and h(t).

ANSWER:

Step 1 of 5

(a)  

Applying Laplace transform for ,

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