Optimum Filtering with a Class of Nonlinear Systems

This paper considers the problem of nonlinear filtering and interpolation of random input in the presence of noise. A special class of nonlinear systems is used which is composed of a linear system in parallel with a zero-memory nonlinearity (ZNL) preceded by a variable delay. The optimization problem is simplified if the inputs are restricted to be of the separable class. The optimum system of this class is shown to be implemented in terms of the optimum linear filter and the optimum ZNL filter. Furthermore, a suboptimal scheme can also be constructed by adding a ZNL to the optimum linear system which improves its performance. The dependence of the error improvement on the delay is also considered, and the best choice of the delay is illustrated by an example.