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Math Help - Basic Fourier Series question

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    Super Member craig's Avatar
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    Basic Fourier Series question

    In comparison to the rest of the question in this section this will hopefully be easier for someone, here goes.

    Let fbe a function with period 2, such that:

     f(x) = \left\{ <br />
  \begin{array}{l l}<br />
    -1 & \quad -1 \leq x < 0\\<br />
    1 & \quad 0 \leq x < 1\\<br />
  \end{array} \right.

    Find the Fourier Series of f.

    f is an odd function so a_0 = a_n = 0, and we know that b_n = 2 \int^1_0 f(x) \sin{\pi n x}.

    I'm just not sure what to put for the f(x), would it be 1 or -1?

    Cheers for the help
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  2. #2
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    Quote Originally Posted by craig View Post
    In comparison to the rest of the question in this section this will hopefully be easier for someone, here goes.

    Let fbe a function with period 2, such that:

     f(x) = \left\{ <br />
  \begin{array}{l l}<br />
    -1 & \quad -1 \leq x < 0\\<br />
    1 & \quad 0 \leq x < 1\\<br />
  \end{array} \right.

    Find the Fourier Series of f.

    f is an odd function so a_0 = a_n = 0, and we know that b_n = 2 \int^1_0 f(x) \sin{\pi n x}.

    I'm just not sure what to put for the f(x), would it be 1 or -1?

    Cheers for the help
    The way you have written it it would need to be 1

    if you used the limits of integration

    2\int_{-1}^{0}f(x)\sin(\pi n x)dx then it would be -1

    both integrals will give the same value.
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  3. #3
    Super Member craig's Avatar
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    Many thanks
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