Some aspects of zero-memory nonlinear filtering

John B. Thomas; Abraham H. Haddad

doi:10.1016/0016-0032(68)90088-4

Some aspects of zero-memory nonlinear filtering

John B. Thomas^*, Abraham H. Haddad

^*Corresponding author for this work

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The general minimum-mean-square error (MMSE) nonlinear filter is tractable if it is restricted or reduced to have no memory. The importance of the zero-memory nonlinear (ZNL) filter is that it is a fundamental building block for more general nonlinear systems. This paper discusses several problems related to ZNL filtering, in particular, one aspect of the prefiltering problem. The general solution of an inverse problem to the prefiltering problem is discussed in detail, and the cases where it assumes a comparatively simple form are treated. Two examples are given to illustrate the characteristics of the nonlinearities and the resulting errors.

Original language	English (US)
Pages (from-to)	98-109
Number of pages	12
Journal	Journal of the Franklin Institute
Volume	285
Issue number	2
DOIs	https://doi.org/10.1016/0016-0032(68)90088-4
State	Published - Feb 1968

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/0016-0032(68)90088-4

Cite this

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title = "Some aspects of zero-memory nonlinear filtering",

abstract = "The general minimum-mean-square error (MMSE) nonlinear filter is tractable if it is restricted or reduced to have no memory. The importance of the zero-memory nonlinear (ZNL) filter is that it is a fundamental building block for more general nonlinear systems. This paper discusses several problems related to ZNL filtering, in particular, one aspect of the prefiltering problem. The general solution of an inverse problem to the prefiltering problem is discussed in detail, and the cases where it assumes a comparatively simple form are treated. Two examples are given to illustrate the characteristics of the nonlinearities and the resulting errors.",

author = "Thomas, {John B.} and Haddad, {Abraham H.}",

note = "Funding Information: The authors wish to express their appreciation to the National Science Foundation and to the U.S. Army Research Of&e-Durham for their generous support of this research under Grant GK-187 and Contract DA-31-124-ARO-D-292, respectively. This is a revised version of a paper presented at the 1966 IEEE Region Six Annual Conference. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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N2 - The general minimum-mean-square error (MMSE) nonlinear filter is tractable if it is restricted or reduced to have no memory. The importance of the zero-memory nonlinear (ZNL) filter is that it is a fundamental building block for more general nonlinear systems. This paper discusses several problems related to ZNL filtering, in particular, one aspect of the prefiltering problem. The general solution of an inverse problem to the prefiltering problem is discussed in detail, and the cases where it assumes a comparatively simple form are treated. Two examples are given to illustrate the characteristics of the nonlinearities and the resulting errors.

AB - The general minimum-mean-square error (MMSE) nonlinear filter is tractable if it is restricted or reduced to have no memory. The importance of the zero-memory nonlinear (ZNL) filter is that it is a fundamental building block for more general nonlinear systems. This paper discusses several problems related to ZNL filtering, in particular, one aspect of the prefiltering problem. The general solution of an inverse problem to the prefiltering problem is discussed in detail, and the cases where it assumes a comparatively simple form are treated. Two examples are given to illustrate the characteristics of the nonlinearities and the resulting errors.

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Some aspects of zero-memory nonlinear filtering

Abstract

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