A computational method for the LU decomposition of rectangular matrices and its implications to the realization of 2-D digital filters

Author

Charalambous, Christakis ; Nashashibi, Adib Y.

Author_Institution

Dept. of Electr. & Comput. Eng., Kuwait Univ., Safat, Kuwait

Volume

40

Issue

11

fYear

1992

fDate

11/1/1992 12:00:00 AM

Firstpage

2789

Lastpage

2798

Abstract

The realization of 2-D digital filters based on the lower-upper triangular decomposition of the coefficient matrix is investigated. A numerical method based on the QA decomposition, which has some important characteristics, is proposed for reaching the LU structure. The coefficients in the final LU structure have values favorable to fixed-point arithmetic implementation. Furthermore, the QR structure can be used for the realization and possesses good numerical characteristics in terms of the approximate decomposition scheme. The symmetry in the impulse response coefficient matrix of an octagonally symmetric 2-D FIR filter is utilized to reduce the computational effort spent in the decomposition and the total number of multipliers in the final realization structure

Keywords

filtering and prediction theory; matrix algebra; two-dimensional digital filters; 2-D digital filters; LU decomposition; QA decomposition; coefficient matrix; computational method; fixed-point arithmetic implementation; impulse response coefficient matrix; lower-upper triangular decomposition; numerical method; octagonally symmetric 2-D FIR filter; rectangular matrices; Digital filters; Finite impulse response filter; Fixed-point arithmetic; Helium; IIR filters; Matrix decomposition; Nonlinear filters; Symmetric matrices; Transfer functions; Transmission line matrix methods;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.165666

Filename

165666