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Fourier Series coefficients, orthogonal?

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Hello. I need help with orthogonality of the fourier series coefficients. I know you can use the dirac delta function, (or the kronecker function) in the orthogonality relationship. I want to try and see the derivation using complex form rather than sines and cosines.

    2. Relevant equations

    proof of
    [itex]\frac{1}{T}\int^T_0 e^{inw_0t}e^{-imw_0t} dt = \delta_{m}{n}[/itex]

    3. The attempt at a solution

    Basically I havent got very far, do not know where to start in this proof. any help would be appreciated?

    thanks
     
  2. jcsd
  3. Oct 19, 2011 #2
    Obviously, m and n must be integers, which makes things really easy. Just assume m=n, do the integration and write down what you get. Then assume [itex] m \neq n [/itex], do the integration and write down what you get.
     
  4. Oct 19, 2011 #3
    Okay I have got it. Thanks!
     
    Last edited: Oct 19, 2011
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