Consider a Linear and Time-Invariant System (LTI) whose impulse response is given by h(t). Find the output y(t) corresponding to the input x(t) using the Convolution Integral x(t) = 2[u(t) - u(t - 3)] + [u(t - 3) - u(t - 5)] h(t) = e^{3t}[u(t) - u(t - 3)]
Added by Juan Luis B.
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First, let's rewrite the input x(t) as a sum of two functions: x(t) = x1(t) + x2(t) where x1(t) = 2[u(t) - u(t - 3)] x2(t) = [u(t - 3) - u(t - 5)] Now, we can find the output y(t) by convolving the input x(t) with the impulse response h(t): y(t) = x(t) * h(t) Show more…
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