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The use of statistical methods of digital signal processing, applied to the shortening of the channel impulse response of data communication systems XDSL (Digital Susbscriber Line) is presented. It approaches the problem of reducing the inter symbol interference (ISI) by modifying the channel impulse response, from its estimation and the formulation of a mathematical model FIR (Finite Impulse Response). As a methodology of work the maximum likelihood method through the recursive algorithm Expectation Maximum (EM) is applied, with modifications directed to improving the erratic behavior of the algorithm (instability and possible non-convergence), for determinated types of signals and data channels. Results obtained from the application of the proposed method in computational models for a system that uses a digital communication channel AWGN dispersive type are shown. The experimental results are in agreement with the analytical estimations expected.