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Fourier Coefficients 
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#1
Aug107, 09:52 AM

P: 464

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? 


#2
Aug107, 04:26 PM

Sci Advisor
P: 6,106

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.



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