A function [tex]f(t)[/tex] can be represented by the expansion [tex] 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) + .... [/tex] Do the constants [tex]A_{n}[/tex] and [tex]B_{n}[/tex] 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?
In computing the Fourier transform, the kernel is of the form e^{inwt}. For A_{0}, the kernel is simply 1, so there is no imaginary part.