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Fourier Series Watch

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    I am having trouble with fourier series, can anyone point me in the right direction with the question. The graph has been attached.

    f(t+3) = f(t)

    The fourier representation of f(t) is given by

    f(t) =ao/2 + ? ancos(2npit/3) + bnsin(2npit/3)

    Determine the coefficient b2

    Thank you.
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    Just an idea. Add one to your function so that it's zero most of the time and =2 for that little bit where -1<x<0.

    Get the Fourier series for that function (much less work) and then subtract 1 from your constant term.
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    (Original post by smarch)
    I am having trouble with fourier series, can anyone point me in the right direction with the question. The graph has been attached.

    f(t+3) = f(t)

    The fourier representation of f(t) is given by

    f(t) =ao/2 + ? ancos(2npit/3) + bnsin(2npit/3)

    Determine the coefficient b2

    Thank you.
    Use the g(t) = f(t)+1 function with 2p=3 period
    and integrate between -p=-3/2 and p=3/2
    So:
    \displaystyle a_0=\frac{1}{p}\int^{p}_{-p}f(t)dt
    \displaystyle a_n=\frac{1}{p}\int^{p}_{-p}f(t)cos\frac{n\pi t}{p}\ dt
    \displaystyle b_n=\frac{1}{p}\int^{p}_{-p} f(t)sin\frac{n\pi t}{p}\dt
    \displaystyle f(t)=-1+\frac{a_0}{2}+\sum^{\infty}_{n  =1}\left( a_ncos\frac{n\pi t}{p}+b_nsin\frac{n\pi t}{p}\right)
 
 
 
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