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We address the problem of modeling received pulse trains in a multipath fading channel and of computing their exact spectrum. We propose a model based on point processes. Such model is very general, simple and tractable and it allows to account for various phenomena that affect the transmission. We then give the exact spectrum of the output of such a model. Spectral formula of specific configurations are then derived from a singular general formula, where the various features of the channel and the pulse transmission appear explicitly.