Fourier Coefficients

  1. A function [tex]f(t)[/tex] 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 [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. jcsd
  3. mathman

    mathman 6,706
    Science Advisor
    Gold Member

    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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