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Unformatted text preview: 1. (10 points) Suppse that the impulse response of a LTI system is given by the following: t h(t)1 1 2 3 4 0.5 1 Draw a plot(include values on both axes) of the output of this system when the following input is applied: x ( t ) = 2 X k =0 δ t 3 k 2 2 2. (10 points) Suppose that the input to a LTI system is given by u ( t + 1) u ( t 1), and that the impulse response of this system is h ( t ) = e 2 t ( u ( t ) u ( t 3)). Determine the output of the system in response to this input by directly evaluating the convolution integral. 3 3. (6 points) Suppose that a continuous time, linear time invariant system is defined by a differential equation of the form d 2 y ( t ) dt 2 + 6 dy ( t ) dt + Ky ( t ) = g ( t ) For what values of K is this system asymptotically stable? 4. (6 points) For each of the following systems, determine whether the system is linear, timeinvariant, or both: (a) y ( t ) = t 2 x ( t 1) (b) y [ n ] = x 2 [ n 2] (c) y [ n ] = x [ n + 1] x [ n 1] 4 5. (10 points) Suppose that a LTI system has the properties that it turns the unit pulse into a triangle as5....
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This note was uploaded on 12/14/2011 for the course BME 343 taught by Professor Emelianov during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Emelianov

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