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at the origin and thus gives for each . This can be summarised by interpreting the Dirac comb as a limit of the Dirichlet kernel such that, at the positions , all exponentials in the sum point into the same direction and add constructively. In other words, the continuous Fourier transform of periodic functions leads to
: with ,and
: The Fourier series coefficients for all when , i.e.
: is another Dirac comb, but with period in angular frequency

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