lecture 23 - Fourier 2

lecture 23 - Fourier 2 - Announcements Prayer...

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Announcements 2/28/11 Prayer My office hours this week:  I’ll likely be in my lab,  room U130, just down the hall from normal office  hour location. Find me there. Exam 2 starts on Saturday Exam review session, results of voting: a. Friday 3:30 – 5 pm.  Room: C261 Next week: I’ll be out of town on Mon. You’ll have  Dr. Gus Hart as a substitute.  
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Summary of last time 0 0 1 ( ) L a f x dx L = 0 2 2 ( )cos L n nx a f x dx L L π = ÷ 0 2 2 ( )sin L n nx b f x dx L L π = ÷ 0 1 1 2 2 ( ) cos sin n n n n nx nx f x a a b L L π π = = = + + ÷ ÷ The series How to find the coefficients
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Fourier Transform (review) Do the transform (or have a computer do it) Answer from computer: “There are several components at different values of k; all are multiples of k=0.01. k = 0.01: amplitude = 0 k = 0.02: amplitude = 0 k = 0.90: amplitude = 1 k = 0.91: amplitude = 1 k = 0.92: amplitude = 1 …” 6 0 0 4 0 0 2 0 0 2 0 0 4 0 0 6 0 0 2 0 1 0 1 0 2 0 C o s 0 . 9 x C o s 0 . 9 1 x C o s 0 . 9 2 x C o s 0 . 9 3 x C o s 0 . 9 4 x C o s 0 . 9 5 x C o s 0 . 9 6 x C o s 0 . 9 7 x C o s 0 . 9 8 x C o s 0 . 9 9 x C o s 1 . x C o s 1 . 0 1 x C o s 1 . 0 2 x C o s 1 . 0 3 x C o s 1 . 0 4
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