In Chapter 3, direct convolution was used to solve for the output of LTI systems. For the...

In Chapter 3, direct convolution was used to solve for the output of LTI systems. For the following inputs and impulse responses, find the output using Laplace transforms.

(a) Problem where x(t) = e–2tu(t) and h(t) = u(t).

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(b) Problem where x(t) = e–tu(t) and h(t) = u(t – 1) – u(t – 3). You may find the time-shift property to be useful.

Consider the integrator in Figure This system is described in Example 3.1 and has the impulse response h(t) = u(t).

(ii) e–2tu(t)

For the system of Figure (a), the input signal is x(t), the output signal is y(t), and the impulse response is h(t). For each of the following cases find y(t):

(d) x(t) = e–tu(t), h(t)= u(t – 1) – u(t – 3).