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ps7 - EE 350 PROBLEM SET 7 DUE 5 November 2007 Reading...

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EE 350 PROBLEM SET 7 DUE: 5 November 2007 Reading assignment: Lathi Chapter 4, Sections 4.1 through 4.4 Laboratory sections will meet during the week of October 29. Problem 33: (20 points) Figure 1 shows a representation of the triangle waveform used in Laboratory #3. Figure 1: A triangle waveform with a fundamental period T o and peak-to-peak amplitude 2 A . 1. (10 points) Determine the trigonometric Fourier series coeﬃcients a o , a n , and b n in terms of T o and A , and if possible, use symmetry properties to simplify the calculations. 2. (4 points) Using the results from part 1, determine the compact trigonometric Fourier series coeﬃcients C n and θ n . 3. (6 points) Using the expressions developed in part 2 to compute the coeﬃcients C n and θ n for the triangle wave used in Laboratory #3, where T o = 1 ms and A = 1 V. Construct the following table to compare your theoretical results to the experimental values obtained in Laboratory #3, where PE = ± | C n | theory -| C n | exp ² | C n | theory × 100 . n Peak Location [kHz] | C n | [V RMS ] PE Theory Experiment 0 1 2 3 4 5

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Problem 34: (20 points) 1. (2 points) When f ( t ) is a real-valued, periodic signal, show that D - n = D * n .
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ps7 - EE 350 PROBLEM SET 7 DUE 5 November 2007 Reading...

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