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314-Quiz1_sol

# 314-Quiz1_sol - z t when the input w t is 1-1 t 1 2 w(t...

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ECEN 314 Quiz # 1 Georghiades September 17, 2008 Note: Quiz is open-book, 15 minutes long. 1. For a linear, time-invariant system, it is known that when the input is x 1 ( t ), the output is y 1 ( t ) and when the input is x 2 ( t ), the output is y 2 ( t ). Find the output, y ( t ), of the system when the input, x ( t ), is: (a) x ( t ) = 2 x 1 ( t - 1) - 3 x 2 ( t - 3) . (b) x ( t ) = 3 dx 1 ( t ) dt + 10 x 2 ( t ) . 2. A linear, time-invariant system, S , has been observed to produce the following input-output signals: 1 1 t x(t) y(t) S 1 1 t 2 Plot the output,
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Unformatted text preview: z ( t ), when the input, w ( t ), is: 1-1 t 1 2 w(t) Solution 1. By linearity and time-invariance, the outputs corresponding to the two inputs are: (a) y ( t ) = 2 y 1 ( t-1)-3 y 2 ( t-3) . (b) y ( t ) = 3 dy 1 ( t ) dt + 10 y 2 ( t ) . 2. The new input can be written as: w ( t ) = x ( t )-x ( t-1) . Thus, the new output is z ( t ) = y ( t )-y ( t-1) . 1-1 t 1 2 z(t) 3 1...
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