Best stable and invertible approximations for ARMA systems

Author

Combettes, Patrick L. ; Trussell, H. Joel

Author_Institution

Dept. of Electr. Eng., City Univ. of New York, NY, USA

Volume

40

Issue

12

fYear

1992

fDate

12/1/1992 12:00:00 AM

Firstpage

3066

Lastpage

3069

Abstract

A method is proposed for finding the best stable and invertible approximations for an autoregressive moving average (ARMA) system, relative to a general quadratic metric in the coefficient space. Mathematically, the problem is equivalent to projecting the regression and moving average vectors of the system onto the set S of coefficients of monic Schur polynomials. The geometry of S is too complex to allow the problem to be approached directly in the ARMA coefficient space. A solution is obtained by constrained steepest descent in the hypercube of reflection coefficients, which is homomorphic to S

Keywords

approximation theory; parameter estimation; polynomials; set theory; signal processing; stability; ARMA systems; autoregressive moving average; coefficient space; constrained steepest descent; convergence; general quadratic metric; hypercube; invertible approximations; monic Schur polynomials; reflection coefficients; set theoretic estimation; stability; Cities and towns; Difference equations; Filters; Geometry; Hypercubes; Polynomials; Reflection; Space stations; Stability; Transfer functions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.175751

Filename

175751