# Fourier Coefficients

by dimensionless
Tags: coefficients, fourier
 P: 464 A function $$f(t)$$ can be represented by the expansion $$f(t) = \frac{1}{2}A_{0} + A_{1}cos(\omega t) + A_{2}cos(2 \omega t) + A_{3}cos(3 \omega t) + .... B_{1}sin(\omega t) + B_{2}sin(2 \omega t) + B_{3}sin(3 \omega t) + ....$$ Do the constants $$A_{n}$$ and $$B_{n}$$ the same thing as the real and imaginary components of the Fourier transform? If so, why is there no imaginary component in the zeroth term?
 Sci Advisor P: 5,891 In computing the Fourier transform, the kernel is of the form einwt. For A0, the kernel is simply 1, so there is no imaginary part.

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