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Unformatted text preview: 1 EE102 Signals and Systems 2010 Fall Midterm Jin Hyung Lee MIDTERM Name: UID: You have 2 hours for 4 problems. 1. Show neat work in the clear spaces on this exam to convince us that you derived, not guessed, your answers. 2. Show your final answers in the boxes at the end of each question. Closed book. Closed notes. You can use one hand-written letter sheet for your reference. Problem Score 1 2 3 4 Total 2 1. Linear Time Invariant System Determine the linearity and time invariance of the systems given below. (a) y ( t ) = x 2 ( t ) + x ( t- 2) + 3 i. Input αx ( t ) into the system, the output is ˆ y ( t ) = α 2 x 2 ( t )+ αx ( t- 2)+3 . ˆ y ( t ) does not equal the scaled output y ( t ) : αy ( t ) = αx 2 ( t ) + αx ( t- 2) + 3 α . So the system is NOT linear. ii. Input delayed signal ˆ x ( t ) = x ( t- T ) . Then, the corresponding output is ˆ y ( t ) = ˆ x 2 ( t ) + ˆ x ( t- 2) + 3 = x 2 ( t- T ) + x ( t- 2- T ) + 3 . iii. Delayed y ( t ) gives: y ( t- T ) = x 2 ( t- T ) + x ( t- T- 2) + 3 , which is equals ˆ y ( t ) ....
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This note was uploaded on 12/13/2011 for the course EE 102 taught by Professor Levan during the Fall '08 term at UCLA.
- Fall '08