Comparing LS FIR filtering and l-step ahead linear prediction

Author

Papaodysseus, Constantin N. ; Carayannis, George ; Koukoutsis, Elias B. ; Kayafas, Eleftherios

Author_Institution

Div. of Comput. Sci., Nat. Tech. Univ. of Athens, Greece

Volume

41

Issue

2

fYear

1993

fDate

2/1/1993 12:00:00 AM

Firstpage

768

Lastpage

780

Abstract

This comparative study of the l-step-ahead linear prediction and least-squares finite impulse response (LS FIR) filtering problems emphasizes the numerical behavior of the resulting Toeplitz systems. It is shown that, although these systems are similar, the restraints on the autocorrelation coefficients fundamentally differentiate them. In the process of doing so, a new algorithmic scheme for the computation of the lagged lattice coefficients is developed, which exhibits fundamentally improved numerical behavior. Moreover, explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm. Finally, the bounds of the LS FIR filter coefficients are treated in comparison with the supremums of the lagged quantities

Keywords

correlation theory; digital filters; filtering and prediction theory; least squares approximations; Toeplitz systems; autocorrelation coefficients; filter coefficients; l-step-ahead linear prediction; lagged lattice coefficients; least squares FIR filtering; least-squares finite impulse response; numerical behavior; supremums; Autocorrelation; Computer science; Filtering; Finite impulse response filter; Lattices; Least squares methods; Nonlinear filters; Predictive models; Symmetric matrices; Vectors;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.193216

Filename

193216