Quiz1_sol - ECEN 314 Solution to Quiz # 1 Georghiades Note:...

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ECEN 314 Solution to Quiz # 1 Georghiades Note: Quiz is open-book, 15 minutes long. 1. A linear, time-invariant system, has the following unit-step response: y ( t ) = e - t - e - 2 t · u ( t ) . Find the following: (a) The impulse-response of the system. (b) The response of the system when the input is: 1 -1 t 1 2 w(t) Solution (a) The unit-impulse function is the derivative of the unit-step function and therefore the impulse response is the derivative of the unit-step response. If we let the impulse response be h ( t ), we have: h ( t ) = dy ( t ) dt = e - t - e - 2 t · | {z } 0 at t =0 δ ( t ) + - e - t + 2 e - 2 t · u ( t ) = 2 e - 2 t - e - t · u ( t ) . The above solution is the fastest for this problem, but not the most general. Since we now know Laplace transforms, there is a much more general way of solving this problem, which works in finding the impulse response when one knows any input-output pair of signals, x ( t ) and y ( t ). The approach is as follows: Take the Laplace transform of the input
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This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.

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Quiz1_sol - ECEN 314 Solution to Quiz # 1 Georghiades Note:...

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