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Fourier series of periodic function

  1. Nov 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Periodic function P=3
    f(t) = 0 if 0<t<1
    1 if 1<t<2
    0 if 2<t<3
    a) Draw the graph of the function in the interval of [-3,6]

    b) Calculate the Fourier series of f(x) by calculating the coefficient.

    2. Relevant equations


    3. The attempt at a solution
    a) in attached file

    b)
    How do I know what is my L?
    L=3/2


    ## \text{ao} = \frac1L \int_0^{3} \left( f(x) \right) dx ##
    ## \text{ao} = \frac1L \int_0^{1} \left( 0 \right) dx + \frac11 \int_1^{2} \left( 1 \right) dx + \frac11 \int_2^{3} \left( 0 \right) dx ##
    ao=2/3

    ## \text{an} = \frac1L \int_1^{2} \left( 1cos(n*pi)/L*x) \right) dx ## n>=1
    an= sin(2*n*pi)/n*pi -sin(n*pi)/n*pi

    ## \text{an} = \frac1L \int_1^{2} \left( 1sin((n*pi)/L*x) \right) dx ## n>=1
    bn= cos(n*pi)/n*pi - cos(2*n*pi)/n*pi
     

    Attached Files:

    Last edited: Nov 29, 2015
  2. jcsd
  3. Nov 29, 2015 #2

    LCKurtz

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    You haven't told us what P is. I suppose it is the period. If so, the P = 3. You also haven't told us what L is defined as. Is it half the period? If so then L = 3/2.
     
  4. Nov 29, 2015 #3
    okay, after I change L for the correct value, is the steps good ?
    is my graph good ?
     
  5. Nov 29, 2015 #4

    LCKurtz

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    Your graph is good. I didn't check your arithmetic.
     
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