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96下信號與系çµ&plusmn

96下信號與系統

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Signals and Systems Midterm 10:20a.m. ~ 12:20p.m., May 2, Fri., 2008 z Closed book, but open 1 sheet (both sides, 2 pages) of personal notes of A4 size z Total score: 120 z Total 4 pages in one B4 sheet 1. [10] Consider a system H to be tested as being memoryless , causal , linear , time invariant , and invertible . Three signals 1 ( ) x t , 2 ( ) x t , and 3 ( ) x t are sent to the system, and the corresponding output signals 1 ( ) y t , 2 ( ) y t , and 3 ( ) y t are obtained as shown in Figure 1. Based on the three input-output pairs, is it possible to determine each of the five properties for system H ? If yes, what is it? If no, why? Justify your answer. Figure 1 2. Consider a system as shown in Figure 2, where ( ) h t is the impulse response of the LTI sub-system in the block, and 2D is the operation of time delay for 2 units. Figure 2 h ( t ) 2D + x ( t ) y ( t ) 1 2 3 4 5 1 2 0 x ( t ) 1 2 3 4 5 1 2 0 h ( t ) H H H 1 2 3 4 5 1 2 3 0 4 x 1 ( t ) 1 2 3 4 5 1 2 3 0 4 x 2 ( t ) 1 2 3 4 5 1 2 3 0 4 x 3 ( t ) 1 2 3 4 5 1 2 3 0 4 y 1 ( t ) 1 2 3 4 5 1 2 3 0 4 y 2 ( t ) 1 2 3 4 5 1 2 3 0 4 y 3 ( t )
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