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Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demonstrate how this expression can be used in the development of an automatic routine , one in which the user needs to specify only the required accuracy.
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D’Amore et al. (1999) studied this question.
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