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Thread: Interval problem in Fourier series

  1. #1
    Member roshanhero's Avatar
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    Aug 2008
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    Unhappy Interval problem in Fourier series

    The functions are-
    $\displaystyle (a) f(x)=\left | x \right |, -\pi\leq x\leq \pi$
    $\displaystyle (b) f(x)=\left | sin x \right |, -\pi\leq x\leq \pi$
    Writing them individually
    a)$\displaystyle f(x)=x $ and $\displaystyle f(x)=-x$
    b)$\displaystyle f(x)=sin x$ and $\displaystyle f(x)=-sin x $
    The problem is what should be the correct intervals for these functions. I am pretty messed up with this basic thing though I can easily compute the fourier series of these functions.
    Last edited by roshanhero; Jul 5th 2010 at 01:05 AM.
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    Basically you need to identify two things:
    1) What values of x make the expression inside the absolute value sign positive?
    2) What values of x make it negative?

    The first problem is simple, but we have to take into account that the domain is $\displaystyle -\pi<x<\pi$.

    $\displaystyle f(x)=|x|=\begin{cases} x, & 0 \le x \le \pi \\ -x, & -\pi \le x < 0 \end{cases}$

    Does this make sense? Can you figure out the second one like this?
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