lecture 22 - Fourier 1

lecture 22 - Fourier 1 - Announcements 2/25/11 Prayer Due...

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Unformatted text preview: Announcements 2/25/11 Prayer Due Saturday night: a. Labs 4-5 b. First extra credit papers - Can do each type of paper once in first half of semester, once in second half c. Term project proposals – Email to me: proposal in body of email, 650 word max. – One proposal per group… but please CC your partner(s) on email . – See website for guidelines, grading, ideas, and examples of past projects. Exam 2 starts next Saturday! a. Exam 2 optional review session: vote on times by Sunday night; I’ll make a decision Monday morning. Anyone need Colton “Fourier series summary” handout? Spectrum Lab on laptop Reading Quiz In the Fourier transform of a periodic function, which frequency components will be present? a. Just the fundamental frequency, f = 1/period b. f and potentially all integer multiples of f c. A finite number of discrete frequencies centered on f d. An infinite number of frequencies near f , spaced infinitely close together e. Masspacity Fourier Theorem Any function periodic on a distance L can be written as a sum of sines and cosines like this: Notation issues: a. a , a n , b n = how “much” at that frequency a. Time vs distance b. a vs a /2 c. 2 π /L = k (or k )… compare 2 π /T = ϖ (or ϖ 0 ) d. Durfee: – a n and b n reversed – Uses λ instead of L The trick: finding the “Fourier coefficients”, a...
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lecture 22 - Fourier 1 - Announcements 2/25/11 Prayer Due...

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