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Math Help - Fourier Series question - finding coefficients

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    Fourier Series question - finding coefficients

    Find the Fourier coefficients of the following equation and write the function as infinite series.

    V = 20 + 10 sin t
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    Re: Fourier Series question - finding coefficients

    Quote Originally Posted by sanka23 View Post
    Find the Fourier coefficients of the following equation and write the function as infinite series.

    V = 20 + 10 sin t
    What have you tried? Where are you stuck?
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    Re: Fourier Series question - finding coefficients

    so far im hovering around these values;

    -5i n = 1
    5i n = -1
    20 n = 0

    but I dont really understand what it is asking me to do when it says ' write the function as infinite series'. Am I just totally off track?
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    Re: Fourier Series question - finding coefficients

    Whether you are "completely off base" depends on exactly what you think a "Fourier series" is! A Fourier series is an infinite series of the form
    \sum_{n= 0}^\infty a_n sin(nx)+ b_n cos(nx)

    However, it is quite possible for most of those coefficients, a_n and b_n, to be 0! In this case, you don't have to do any "calculation" at all- just compare
    \sum_{n= 0}^\infty a_n sin(nx)+ b_n cos(nx)
    and 20+ 10 sin(t).
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    Re: Fourier Series question - finding coefficients

    Quote Originally Posted by HallsofIvy View Post
    Whether you are "completely off base" depends on exactly what you think a "Fourier series" is! A Fourier series is an infinite series of the form
    \sum_{n= 0}^\infty a_n sin(nx)+ b_n cos(nx)

    However, it is quite possible for most of those coefficients, a_n and b_n, to be 0! In this case, you don't have to do any "calculation" at all- just compare
    \sum_{n= 0}^\infty a_n sin(nx)+ b_n cos(nx)
    and 20+ 10 sin(t).
    Hi. I'm trying to learn Fourier Series (and the transform, too). This thread touches on a couple of questions I have, may I post them here?

    The definition I have for the Fourier Series, g(t) (with P as the fundamental period), is:
    g(t)=\sum_{n=-\infty}^{\infty} c_n \cdot e^{i\frac{2 \pi n t}{P}}

    where c_n is (using v(t) as the original equation from the OP):
    c_n=\frac1T \int_0^T v(t) \cdot e^{-i\frac{2 \pi n t}{P}}dt

    I can use Euler's identity to get your definition, but you are starting your series at 0, the definition I have starts at -\infty. Why the indexing difference?

    Using your definition, shouldn't a_n=b_n for all n? If your definition comes from my definition and Euler's identity, the coefficients would be the same.

    Last, I tried (for practice) the problem from the OP, using P=\pi as the fundamental period). I tried comparing v(t)=20+10sin(t) to your series definition. I get:
    a_1=10
    a_n=0\; \forall n \ne 1
    b_n=0\; \forall n.

    Is that right? If so, what is the final answer (the infinite Fourier Series)? What about the 20 in original equation?

    I also tried the definition I have for c_n. But those integrations return very complicated answers (I used Maple to calculate them), and nothing like what I have in the last paragraph. Why doesn't that integration turn up the same results?

    Thanks, in advance, for anyone who replies.
    Last edited by MSUMathStdnt; August 13th 2011 at 04:01 PM.
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  6. #6
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    Re: Fourier Series question - finding coefficients

    HallsOfIvy posted the definition of a fourier series on real form. You have the complex form.

    Complex Form of Fourier Series
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