Nonlinear infinite extent interpolation of stationary processes

Author

Bondon, Pascal ; Bourin, Christophe

Author_Institution

Lab. des Signaux et Syst., CNRS, Gif-sur-Yvette, France

Volume

45

Issue

12

fYear

1997

fDate

12/1/1997 12:00:00 AM

Firstpage

3039

Lastpage

3052

Abstract

The problem of minimum mean-square interpolation of discrete time stationary stochastic processes using a system consisting of a finite number p of nonlinear instantaneous transformations followed by a p input-one output infinite extent linear filter is studied. The expressions of the optimal interpolator and of the approximation error are derived and generalize the corresponding relations known in linear interpolation theory. Some extensions, including the estimation problem with several missing observations, are also investigated

Keywords

discrete time filters; error analysis; estimation theory; interpolation; least mean squares methods; nonlinear filters; signal processing; transforms; approximation error; discrete time stationary stochastic processes; estimation problem; linear filter; linear interpolation theory; minimum mean-square interpolation; missing observations; nonlinear infinite extent interpolation; nonlinear instantaneous transformations; optimal interpolator; stationary processes; Approximation error; Bonding; Equations; Fourier transforms; Hilbert space; Interpolation; Nonlinear filters; Random variables; Space stations; Stochastic processes;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.650263

Filename

650263