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Math Help - Need help with a Fourier series

  1. #1
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    Need help with a Fourier series

    The original problem is: f(x) = x if -pi<x<0, and f(x) = pi - x if 0<x<pi. I'm supposed to model this as a Fourier series. I got the sine series correct, but for some reason, when I try to calculate the cosine series as 1/pi * integral[f(x)*cos(nx) dx, -pi, pi], I keep coming up with zero. I cannot spot my error. I don't know if the issue is setting it up, the integration by parts, or what.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Need help with a Fourier series



    \frac{1}{\pi }\int _{-\pi }^{\pi }f(x) \cos (n x)dx = \frac{-\pi  n \sin (\pi  n)-2 \cos (\pi  n)+2}{\pi  n^2}

    \mathcal{F}_x[f(x)](\omega ) = -\frac{e^{-i \pi  \omega } \left(-1+e^{i \pi  \omega }\right) \left(-1+e^{i \pi  \omega }-i \pi  \omega \right)}{\sqrt{2 \pi } \omega ^2}
    Attached Thumbnails Attached Thumbnails Need help with a Fourier series-fourier-series.png  
    Last edited by MaxJasper; October 6th 2012 at 08:11 PM.
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  3. #3
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    Re: Need help with a Fourier series

    Yeah, I mean, even a casual inspection of that graph reveals that the cos series can't be zero.

    I probably just made a careless mistake or two; I'll go back (again) and review my work.

    EDIT: Wait a minute. Isn't sin(n*pi) = 0 whenever n is an integer, which is the case with Fourier?
    Last edited by phys251; October 6th 2012 at 09:48 PM.
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