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Understanding of the fourier coefficients?

  1. Apr 21, 2007 #1
    Im just looking through examples of finding the fourier coefficients.

    in one particular example bn is found to be = (-1/npi) (cosnpi - cos 0)

    then it says this is 0 when n is even
    and 2/npi when n is odd

    are we just substituting values of n e.g. 1,2,3..... to find this result?

    i apologise if i am doing something stupid with my calculation but when i put even numbers in place of n i do not get 0 as it states i should?
  2. jcsd
  3. Apr 21, 2007 #2


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    cos(n*pi) - cos(0) = cos(n*pi) - 1 = (-1)n - 1

    (-1)n = 1 when n is even and -1 when n is odd.
    So when n is even: 1-1 = 0, when odd: -1-1 = -2
    These are of course divided by -n*pi to get bn.
    Last edited: Apr 21, 2007
  4. Apr 21, 2007 #3


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    cosine of an odd multiple of [itex]\pi[/itex] is -1 and cosine of an even multiple of [itex]\pi[/itex] is 1. That's exactly what they are doing.
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