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Math Help - Fourier Series involving modulus

  1. #1
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    Smile Fourier Series involving modulus

    Hi,

    I have this question:

    Calculate the fourier series for g(t) = 2 - 2|cos(t/2)|

    I've sketched the graph so I know that that the function is even, meaning that bn=0, and it has period of 2*pi (from -pi to pi). However i just can't seem to work out how to deal with the modulus. I think i have to split the integrals into two parts, is this right?

    Please help,
    Katy
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  2. #2
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    Quote Originally Posted by harkapobi View Post
    Hi,

    I have this question:

    Calculate the fourier series for g(t) = 2 - 2|cos(t/2)|

    I've sketched the graph so I know that that the function is even, meaning that bn=0, and it has period of 2*pi (from -pi to pi). However i just can't seem to work out how to deal with the modulus. I think i have to split the integrals into two parts, is this right?

    Please help,
    Katy
    Yes, of course, just like you always do with absolute values, do x< 0 and x> 0 separately.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    Yes, of course, just like you always do with absolute values, do x< 0 and x> 0 separately.
    I thought so. I may be being really dumb here, but I really can't figure out how this affects the integrals. Would it be:

    2 - 2 cos(t/2) for t>0
    2 + 2cos(t/2) for t<0 ?
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