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In this paper we develop optimal recursive waveshaping filters in the framework of estimation theory and state-variable models. We develop a linear minimum-variance waveshaper and a nonlinear maximum-likelihood waveshaper. Both waveshapers are comprised of two components:(1) stochastic inversion and (2) waveshaping. The former is performed by means of minimum-variance deconvolution. Simulation results are given which illustrate results that can be obtained by both waveshapers. In retrospect, we view the minimum-variance results of this paper as the recursive counterparts to those presented by Treitel and Robinson (13), which are for finite-impulse response waveshaping.