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# 301 - NAME ECE 301 Division 2 Exam 1 Solutions This is a...

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-1 0 1 2 3 4 0 0.5 1 1.5 2 t x 1 (t) -1 0 1 2 3 4 0 0.5 1 1.5 2 t y 1 (t) x 1 response to x 1 -1 0 1 2 3 4 0 0.5 1 1.5 2 t x 2 (t) -1 0 1 2 3 4 0 0.5 1 1.5 2 t y 2 (t) x 2 response to x 2 -1 0 1 2 3 4 0 0.5 1 1.5 2 t x 3 (t) -1 0 1 2 3 4 0 0.5 1 1.5 2 t y 3 (t) x 3 response to x 3 Figure 1: Three input signals for Problem 1 (left column) and the corresponding system responses (right column). Problem 1 (10 points). Three input-output pairs for a system are given in Fig. 1: the responses of the system to the input signals x 1 , x 2 , and x 3 , are, respectively, y 1 , y 2 , and y 3 . All these six signals are zero for t < - 1 and for t > 4. Assume that x 1 (0) = x 2 (0) = x 3 (2) = y 3 (2) = 1 and that x 1 (1) = x 2 (2) = x 3 (3) = y 1 (1) = y 2 (2) = y 3 (3) = 0. It is given that the system is linear. Answer each of the following multiple-choice questions by circling the correct answer. a (2 points). A. The system is memoryless. B. The system could be memoryless. C. The system is not memoryless. b (2 points). A. The system is causal. B. The system could be causal. C. The system is not causal. 2
c (2 points). A. The system is BIBO stable. B. The system could be BIBO stable. C. The system is not BIBO stable. d (2 points). A. The system is time-invariant. B. The system could be time-invariant. C. The system is not time-invariant. e (2 points). Given the following input signal x ( t ) = 1 , 0 t < 1 2 , 1 t < 2 0 , otherwise A. the system’s response to x is y A ( t ) = 1 , 0 t < 1 2 , 1 t < 2 0 , otherwise B. the system’s response to x is y B ( t ) = t, 0 t < 1 2 , 1 t < 2 0 , otherwise C. the system’s response to x is y C ( t ) = t, 0 t < 1 1 , 1 t < 2 0 ,

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301 - NAME ECE 301 Division 2 Exam 1 Solutions This is a...

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