On a class of infinite extent nonlinear interpolators

The problem of minimum mean-square (m.s.) interpolation of a discrete-time stationary stochastic process using a class of infinite extent nonlinear interpolators is studied. These interpolators consist of a finite number p of nonlinear instantaneous transformations followed by a p input one output infinite extent linear filter. The expressions of the optimal interpolator and of the approximation error are derived and generalize the corresponding relations known in linear interpolation theory. As an extension, the estimation problem with several missing observations is also investigated.