MIT
18 06 -
Lecture 18
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Lecture 18 Fourier Series Orthogonal basis in function space Example One basis is 1 x x x But this basis is not orthogonal Dot Product of f x and g x If the dot product is zero the functions are orthogonal f g f x g x x We want to add all f x and g x where 0 x 2 Fourier basis 1 cosx sinx cos2x sin2x They are orthogonal Example Find a2 Find a2 Fourier Coef cients Complex Fourier basis 1 e e e e e Euler Dot product for complex numbers use the complex conjugate
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