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In our previous work (2003), we investigated a new approach to robust speech recognition. An exact procedure was developed to filter noisy cepstral coefficients in the mean-square-error sense, and it was shown that this method outperformed the well known vector Taylor series (VTS) approach, which in turn is based on linear approximations to the non-linear filtering problem. Unfortunately. the procedure presented involved several integral equations with no known closed form solution. Numerical integration techniques were needed, which in turn led to slow performance, and in some cases, numerical problems. In this work we address this problem by using piecewise approximations to the integrands, which in turn yield closed form solutions. The revised procedure is tested on a subset of the Aurora 2 database, and the results are compared with the original numerical integration based approach, as well as VTS.