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Unformatted text preview: ECE 220, Section 051 Problem Lab Number 8 Chapter 9, Fourier Series and a Review of Laplace Transforms Due Week of July 20, 2009 The goal of this lab is to cover Chapter 8 (Laplace Transforms) and Chapter 9 (Fourier Series). We start with Chapter 9 on Fourier Series and then cover some problems from Chapter 8 as a review. Work out as many problems as you can. If you have worked on a problem before, or are comfortable with that type of problem, skip it and go to one you are less familiar with. Do not worry if you do not finish all problems in the lab time (though make sure you can do these problems as review material for the test). Part I. Fourier Series and Properties Problem 1) The Fourier Series coefficients, S ( n ) , of a signal s ( t ) with period T = 4 seconds, are given below S ( n ) = e j n 4 sin( n 4 ) n Evaluate the DC component and second harmonics of this signal. Express them in exponential format. Ans: Plug in n { 2 , , 2 } to get S ( 2) , S (0) , S (2) S (0) = 4 S (2) = j 2 S ( 2) = conj ( S (2)) = j 2 Use LHospitals rule to find S (0) . Problem 2) The Fourier Series coefficients, S ( n ) , of a signal s ( t ) with period T = 4 seconds, are given below: S ( n ) = e j n 2 sin( n 4 ) n 4 Approximate the signal in the time domain, by using only the first three terms of the Fourier Series (i.e., only the DC, fundamental and second harmonic). In your final answer, express the signal s ( t ) as a realvalued function of t (i.e., no complex numbers should be present). 1 Ans: Plug in n { 2 , 1 , , 1 , 2 } to get S ( 2) , S ( 1) , S (0) , S (1) , S (2) S (0) = 1 S (1) = j 2 2 S ( 1) = j 2 2 S (2) = 2 S ( 2) = 2 Use LHospitals rule to find S (0) ....
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 Summer '08
 NILSON

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