On optimal and suboptimal nonlinear filters for discrete inputs

The determination of minimum-mean-squared-error (MMSE) nonlinear filters usually involves formidable mathematical difficulties. These difficulties may be bypassed by restricting attention to special classes of filters or special processes. One such class is Zadeh's class
n_{1}
, which for the general case also involves mathematical difficulties. In this work two realizations of class
n_{1}
are used for the MMSE reconstruction and filtering of a sampled signal. The cases where the filter reduces to a zero-memory nonlinearity followed by a linear filter are discussed. A suboptimum scheme composed of a zero-memory nonlinearity followed by a linear filter is considered for the reconstruction and filtering of a subclass of the separable process.