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Fourier Series Transform Proof Help

  1. Feb 7, 2008 #1
    Can someone fill in the blank between these two steps? I can't find fourier series proof anywhere and my professor just left it out.

    (1) y(t+nT)=y(t)

    (2) y(t)=[tex]A_{0}[/tex] + [tex]\Sigma^{\infty}_{n=1}[/tex][[tex]A_{n}[/tex]cos(n[tex]\omega[/tex]t) + [tex]B_{n}[/tex]sin(n[tex]\omega[/tex]t)]

    (The omega is going crazy on me... it's not supposed to be superscripted, just multiplied by n and t)
  2. jcsd
  3. Feb 8, 2008 #2


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    What do you mean by "steps between them"? The first just says y is periodic with period T and the second is the general expression of a Fourier series of a function periodic with period [itex]2\pi/\omega[/itex]- there is no mention of "T".

    As for the LaTex, I would recommend putting the entire thing in [ t e x] not just individual parts:

    [tex]y(t)=A_{0}+ \Sigma^{\infty}_{n=1}[A_{n}cos(n\omega t) + B_{n}sin(n\omega t)][/tex]

    It looks better and is easier to type!
  4. Feb 8, 2008 #3
    I would say that a general "Fourier expansion" is actually an integral. What (1) implies is that the modes are discrete and thus the integral becomes a sum, and therefore [itex]\omega=2 \pi/T [/itex], as Halls mentioned. Maybe this is the missing step you mean?
    Last edited: Feb 8, 2008
  5. Feb 28, 2010 #4
    have u find the gap between those two statements[evotunedscc]?
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