b09hwk3final

# b09hwk3final - ECE2311 HOMEWORK 3 B09 Name ECE Box Number...

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Unformatted text preview: ECE2311 HOMEWORK # 3 B09 Name : ECE Box Number: Due date: This assignment is due Wednesday, November 18, bring to class. Make a photocopy for your reference for fast comparison to solution set. Put all answers on the lines provided! Attach any work sheets with a staple. Problem 1 w Trigonometric Fourier Series In this problem you will construct the Trignometric Fourier Series for a periodic function. The function x(t) has a period of 4 seconds and can be described over the full cycle that takes place from —2 to 2 second by the following function: 0 —2<tg—§ w): 2 —§<tg§ 0 2:32 a) Find the (Lo Fourier trigonometric series coefﬁcient: CLO: b) Find the an Fourier trigonometric series coefﬁcient expression (that is, the function that give an for any n : 1,2, : c) Find the bn Fourier trigonometric series coefﬁcient expression for any n = 1, 2, bn = (1) Generate a table of the coefﬁcient values (four digits of precision) for each indicated in this table by ﬁlling in the missing entries in the table: 11 an bn | #cotoi—I Oi e) Explain which of the results in the table could have been predicted from any symmetry (if there is any) that the function :v(t) possesses. Problem 2 — ’I‘rigonometric Fourier Series (Again) In this problem you will again construct the Trignometric Fourier Series for a periodic function for a function that arises in power supplies that must convert an AC power source into a source of DC power. The function :I:(t) is a “half wave rectiﬁed sinusoid” and has a period of 4 seconds and can be described over the full cycle that takes place from —2 to 2 second by the following function: 0 -—2<t£0 x(t) = 0 < t g 2 b) Find the an Fourier trigonometric series coefﬁcient expression (that is, the function that give an for any n : 1,2, : an : c) Find the b” Fourier trigonometric series coefﬁcient expression for any n = 1, 2, b”: d) Generate a table of the coefﬁcient values (four digits of precision) for each indicated in this table by ﬁlling in the missing entries in the table: n on bn JACON CJ‘I e) Explain which of the results in the table could have been predicted from any symmetry (if there is any) that the function \$(t) possesses. Problem 3 — Compact Fourier Series For the signal you analyzed in Problem 1, give the values or expressions for the compact Fourier coefﬁcients requested below: a) Find the CO Fourier compact trigonometric series coefﬁcient: 00: b) Find the C7, Fourier compact trigonometric series coefﬁcient expression (that is, the function that give 0,, for any n z: 1, 2, 2 C71 2 c) Find the 6),, Fourier compact trigonometric series coefﬁcient expression for any n = 1, 2, 67L 2 (1) Sketch the amplitude spectrum for this function here: Problem 4 — Exponential Fourier Series Analyze the function in Problem 1 again by this time ﬁnd all the coefﬁcients using the intergrals that directly generate the exponential fourier series coefﬁcients. Find the 1),, Fourier trigonometric series coefﬁcient expression (that is, the function that give an for any n : — 2, —1,0, 1,2, : D71, 2 b) Find the numerical value of D0, showing work: 0) Generate a table of the coefﬁcient values (four digits of precision) for each indicated in this table by ﬁlling in the missing entries in the table. Since Dn is in general complex, you will have to give both its magnitude and its phase: m”; 11),, _l cowa OEOT>> Problem 7 - Matlab Fourier Plot Construction Read pages 621-622 and 662—664 of the textbook if you have not yet done so. Modify the example Matlab code in Section M6.1 no page 663 to use the formula for Dn that you found above and to plot this sum for terms 72 : —100...100. Attach the resulting plot. 3eX (b) What is the cause of the overshoot you see in your results. ...
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## This note was uploaded on 04/21/2010 for the course ECE 2311 taught by Professor Hakim during the Winter '08 term at WPI.

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b09hwk3final - ECE2311 HOMEWORK 3 B09 Name ECE Box Number...

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