Title :
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
fDate :
12/1/1992 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
