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Fourier Series and orthogonality
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[QUOTE="ElijahRockers, post: 5029385, member: 321900"] If that's a little wordy for you, maybe I can dumb it down. Just keep in mind I am only now learning this stuff myself. Remember how you used {i, j, k} to represent orthogonal unit vectors? It's the same idea with {cos(x), cos(2x), ... , cos(Nx)}. The same way you could represent any 3D vector as xi + yj + zk, you can represent any function as a sum of sines and cosines of varying frequency. cos(1x) is orthogonal to cos(.9999x) -> meaning the slightest variation in frequency will result in a pair of orthogonal functions... I think. Anyone in the know, please feel free to correct or confirm my suspicions. EDIT: Cut out some stuff I wrote that was even confusing to me. [/QUOTE]
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