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An optimal detector for a known signal in Laplace noise is determined. The analysis starts with a sampled digital receiver, leading to an asymptotic analysis when the number of samples approaches infinity. The optimum detector for Laplace noise achieves twice the signal-to-noise ratio of the matched filter for Gaussian noise. The theoretical analysis is corroborated by computer simulations.
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Beaulieu et al. (2013) studied this question.
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