Nonlinear Prediction of a Class of Random Processes

A. H. Haddad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper is concerned with the minimum mean-squared error (MMSE) nonlinear prediction of a class of random processes. A class of random processes is defined by the property that its MMSE zero-memory predictor is represented by a finite sum of separable terms. Sufficient conditions for the existence of such processes are also considered. The nonlinear predictor is restricted to be composed of a linear filter in parallel with a zero-memory nonlinearity (ZNL) preceded by a variable delay. The optimum predictor is shown to be the solution of linear integral equations with the same kernel as for the optimum linear predictor. The first step of the derivation also yields a simpler scheme which only requires the addition of a ZNL to the optimum linear predictor. The improvements in the MMSE of the two nonlinear systems over the linear case are compared and illustrated by a numerical example.

Original languageEnglish (US)
Pages (from-to)664-668
Number of pages5
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - Sep 1968

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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