102_1_midterm

# 102_1_midterm - Systems and Signals EE102 Lee Spring...

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Systems and Signals Lee, Spring 2009-10 EE102 Midterm Exam NAME: You have 2 hours for 4 problems. Show neat work in the clear spaces on this exam to convince us that you derived, not guessed, your answers. Put your final answers in the boxes at the bottom of the page. Closed book. Closed notes. You can use one hand-written letter sheet for your reference. Problem Score 1 2 3 4 Total 1

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Problem 1. Computing Fourier Transforms (30 points) The signal f ( t ) is plotted below: 0 2 - 2 t f ( t ) 1 - 4 4 6 - 6 It consists of the signal u ( t ) e - t/ 2 that has been shifted, and a shifted and reversed version of the same signal. a) Find an expression for f ( t ) f ( t ) = 2
b) Find F ( ), the Fourier transform of f ( t ). Make sure to simplify your answer. F ( ) = 3

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Problem 2. Properties of convolution (20 Points) Determine whether the assertions are true or false, and provide a supporting argument. a) The convolution of two odd signals is an odd signal. The assertion is (circle one) true false b) If ( f * g )( t ) = h ( t ), and f d ( t ) = f ( t - a ), and g d ( t ) = g ( t - b ), then ( f d * g d )( t ) = h ( t - b - a ) .
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