Minimum-variance and maximum-likelihood recursive waveshaping

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 consist of two components: 1) stochastic inversion and 2) waveshaping. The former is performed by means of minimum-variance deconvolution. Simulations 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 [14], which are for finite-impulse response waveshaping.