102_1_midterm_practice_solution

# 102_1_midterm_practice_solution - Systems and Signals Lee...

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Unformatted text preview: Systems and Signals Lee, Spring 2009-10 EE102 Midterm Practice Problems Solutions Problem 1. Computing Fourier Transforms The signal f ( t ) is plotted below: f ( t ) t 1 1- 1- 2- 3 2 3 2- 1 a) Find an expression for f ( t ) in terms sums and convolutions of signals defined for all t such as rect( t ) and Δ( t ) ( i.e. do not express it as a piecewise signal, defined over intervals). Solution: There are several solutions. Two simple examples are f ( t ) = 2Δ( t )- Δ( t- 1)- Δ( t + 1) and f ( t ) = 4Δ( t )- 2Δ( t/ 2) b) Find the Fourier transform of f ( t ). Simplify your answer. Solution: The Fourier transform of the first solution is F ( jω ) = 2sinc 2 ω 2 π- e jω sinc 2 ω 2 π- e- jω sinc 2 ω 2 π which can be simplified to F ( jω ) = 2sinc 2 ω 2 π (1- cos( ω )) . The second solution has the Fourier transform F ( jω ) = 4sinc 2 ω 2 π- 4sinc 2 ω π . 1 Problem 2. Fourier Series a) You compute the Fourier series of a signal f ( t ) using a period T . You find that all....
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102_1_midterm_practice_solution - Systems and Signals Lee...

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