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Homework Help: Fourier series coefficient (half range)

  1. Jun 7, 2013 #1
    1. The problem statement, all variables and given/known data

    f(x) = 1, 0<x<1

    Extend f(x) t generate an even function P(x) and find Fourier coefficients

    2. Relevant equations

    an = 2/T ∫ P(x)cos(2nx/T) dx

    3. The attempt at a solution

    P(x) = 1, -1<x<1
    0, -2<x<-1 , 1<x<2

    even function so b0 = 0

    Average of P(x) over T = 0.5

    an = 2/n∏ sin (n∏x)

    I got right upto here...

    answer for the exercise says

    an = 0 when n even
    2/n∏ when n=1,5,9,13...
    -2/n∏ when n = 3,7,11,15...

    I am confused because isnt all mutiples of pi in a sine function all equal to 0?

    Please help :(
    Last edited: Jun 7, 2013
  2. jcsd
  3. Jun 7, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What does T represent and what is it in this problem? Is it the full period? If so, with your choice of P(x), apparently T= 4? Is that what you used in your formulas? If you are going to extend f(x) = 1 on (0,1) to an even function, why not just use f(x) = 1 on (-1,1) for your function? I don't think you have given us a complete statement of the problem.
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