exam1_practice_solutions

Exam1_practice_solut - 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

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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, time-invariant, 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.

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Exam1_practice_solut - 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

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