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November 5th, 2009

Series Parts

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Series Parts

In fourier series...?

why is the complex fourier series "parts" e^p added from N= -infinity to infinity, whereas the real fourier series parts are added only from N=0 to N=infinity?
damn, it's so obvious now. Thanks guys, wish I could give you both best answers

The discrete real fourier series is of the form

∑(A Sin(nx) + B Cos(nx))

If n were to vary from -≈ to ≈, then we'd end up with:

∑(A' Sin(nx) + B' Cos(nx))

where n varies from 0 to ≈. In other words, the terms where n is negative aren't indepedent from the terms where n is positive.

On the other hand, the discrete complex fourier series is of the form:

∑(C e^(inx))

so that e^(inx) and e^(-inx) do not add or cancel out. Thus, all values of n from -∞ to ∞ are independent "orthogonal" components.

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