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midterm - y ( t ) = tan-1 ( x ( t )) , is the system...

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MAE143 A - Signals and Systems - Winter 11 Midterm, February 2nd Instructions (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a hand calculator with no communication capabilities (ii) You have 50 minutes (iii) Do not forget to write your name, student number, and instructor 1. Signals Consider the following mathematical description of a continuous-time signal x ( t ) = u ( t - 1) - (1 - e - ( t - 2) ) u ( t - 2) - δ ( t + 1) . Sketch the plot of the following derived signals: (a) (2 points) x ( t ) (b) (2 points) x (2 - t ) (c) (2 points) x ( t/ 2) 2. System Properties A system takes as input the signal x ( t ) and produces as output y ( t ) . Provide a detailed answer to the following question regarding properties of the systems: (a) (2 points) If
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Unformatted text preview: y ( t ) = tan-1 ( x ( t )) , is the system linear? Is it invertible? (b) (2 points) If y ( t ) = 1 t R t x ( ) d is the system linear? Is it time-invariant? (c) (2 points) If y ( t ) + y ( t ) = x ( t ) is the system linear? Is it BIBO stable? 3. Impulse Response An LTI system is described by the ODE y 00 ( t ) + y ( t ) = x ( t ) (a) (3 points) Compute the impulse response h ( t ) . Use your answer to determine if the sys-tem is BIBO stable. (b) (3 points) Use the impulse response h ( t ) and the convolution formula to compute y ( t ) when x ( t ) = e-2 t u ( t ) . (c) (4 points (bonus)) Use Laplace transforms to compute the answer to the above items (a) and (b)....
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