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Midterm 2 Solutions

# Midterm 2 Solutions - Systems and Signals EE102 Lee Fall...

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Systems and Signals Lee, Fall 2011-12 EE102 Midterm Exam 2 NAME: ID: You have 2 hours for 4 questions. Show enough (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 notes, closed book, 1 letter sized sheet allowed. Problem Score 1 2 3 4 Total 1

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Problem 1. (25 Points) Please use scaled and shifted Δ( t ) and rect ( t ) to express the following signal. (10 pts) Please also show what is the Fourier transform for this signal?(15 pts) 1 2 3 -1 -2 -3 1 2 x(t) Solution: The original signal can be decomposed into three signals: 1 2 3 -1 -2 -3 1 2 x ( t ) = 2Δ( 1 2 ( t - 1)) + 2Δ( 1 2 ( t + 1)) - rect ( 1 2 t ) (10 pts) By using the properties of Fourier transform, X ( ) = ( e - + e )( 4 sin 2 ω ω 2 ) - 2 sinω ω 2
Problem 2. (25 Points) Find out the Fourier transform of the following signals. 1. sinc ( 2 π ω 0 t ) cos ( ω 0 t ) sin ( ω 0 t ) (13 pts) Solution: The Fourier transform for sinc ( 2 π ω 0 t ) is ω 0 2 π rect ( ω 0 4 π 2 ω ) The Fourier transform for cos ( ω 0 t

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Midterm 2 Solutions - Systems and Signals EE102 Lee Fall...

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