Chap4 Lec8 Fourier Series (Student)

Chap4 Lec8 Fourier Series (Student) - HUT – DEPARTMENT OF...

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Unformatted text preview: HUT – DEPARTMENT OF MATH. APPLIED ---------------------------------------------------------------------------------------------------------- IDE – ADVANCED PROGRAM CHAPTER 4: FOURIER SERIES • PhD. NGUYEÃN QUOÁC LAÂN (11/2007) CONTENTS------------------------------------------------------------------------------------------------------------------------------- 8.1 EXPRESSING A FUNCTION IN A TRIGONOMETRIC SERIES 8.2 FOURIER COEFFICIENTS 8.3 FOURIER SERIES OF EVEN AND ODD FUNCTION 8.4 FOURIER SERIES ON HALF – RANGE. EXTENSION 8.5 ORTHOGONAL EXPANSION BEGINNING PROBLEM------------------------------------------------------------------------------------------------------------------------------------ Express a given function f(x) in the trigonometric serie: { }{ } [ ] [ ] π π , , sin cos 2 ) ( : , Find 1- ∈ + + = ∑ ∞ = x nx b nx a a x f b a n n n n n The trigono. system {sinnx, cosmx}, m, n ≥ 0 is orthogonal with respect to the integral scalar product: u ⊥ v ⇔ (u,v) = 0 m n dx mx nx , sin cos 2200 = ∫- π π = = ≠ = ≠ = ∫- , 2 , , cos cos m n m n m n dx mx nx π π π π = ≠ = ∫- m n m n dx mx nx , , sin sin π π π FOURIER COEFFICIENTS------------------------------------------------------------------------------------------------------------------------------------...
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This note was uploaded on 11/02/2009 for the course ECE ece464 taught by Professor Abc during the Spring '09 term at Jacksonville College.

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Chap4 Lec8 Fourier Series (Student) - HUT – DEPARTMENT OF...

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