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Unformatted text preview: UCSB Fall 2006 NAME: PERM NO.: ECE 130A: Final Examination Problems INSTRUCTIONS: Problems are weighted as shown. Answers should be given on these sheets. Show your work. No credit without proper justification, even if your answers are correct. The exam is closed book, closed notes, except for the sheet of formulas provided separately, and the two sides of handwritten notes that you are allowed to bring. Problem 1 (20 points): The output y ( t ) of a system with input x ( t ) is given by y ( t ) = t +2∞ x 2 ( τ ) dτ 1(a) (10 points) True or False The system is causal. (no credit without proper justification) 1(b) (10 points) True or False The system is timeinvariant. (no credit without proper justi fication) NAME: PERM NO.: Problem 2 (10 points): Let x 1 ( t ) = 2 I [0 , 1] ( t ) I [1 , 2] ( t ), and x 2 ( t ) = 3 I [2 , 3] ( t ). Find and sketch the convolution y ( t ) = ( x 1 * x 2 )( t ). NAME: PERM NO.: Problem 3 (40 points): Consider the signal x ( t ) = sinc(8( t + 2))....
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 Fall '07
 MADHOW
 LTI system theory, proper justification

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