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In this paper, we present a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithms described here have closed form solutions for the SISO case. However, for the MIMO case, a set of pre-computed scenarios is used to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. Comparisons are made with other algorithms that have been previously described in the literature as well as with the implementation of algorithms based on the Quasi-Newton method.