Uniqueness of a two-step predictor based spectral estimator that generalizes the maximum entropy concept

Author

Shim, Theodore I. ; Pillai, S. Unnikrishna ; Lee, Won Cheol

Author_Institution

Dept. of Electr. Eng., Polytech. Univ., Brooklyn, NY, USA

Volume

41

Issue

9

fYear

1993

fDate

9/1/1993 12:00:00 AM

Firstpage

2942

Lastpage

2946

Abstract

Given a finite set of autocorrelations, it is well known that maximization of the entropy functional subject to this data leads to a stable autoregressive model. Since maximization of the entropy functional is equivalent to maximization of the minimum mean square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the k-step minimum-mean-square prediction error subject to the given autocorrelations has been shown to result in stable autoregressive moving-average (ARMA) extensions. The uniqueness of this true generalization of the maximum-entropy extension is proved here by a constructive procedure in the case of two-step predictors

Keywords

entropy; filtering and prediction theory; parameter estimation; signal processing; spectral analysis; stochastic processes; ARMA; autocorrelations; autoregressive moving-average; entropy functional; k-step minimum-mean-square prediction error; maximization; maximum-entropy extension; spectral estimator; stable autoregressive model; two-step predictor; Autocorrelation; Density functional theory; Entropy; Mean square error methods; Polynomials; Signal analysis; Stochastic processes; Tires;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.236517

Filename

236517