Weighted low-rank approximation of general complex matrices and its application in the design of 2-D digital filters

Author

Lu, W.-S. ; Pei, S.-C. ; Wang, P.-H.

Author_Institution

Dept. of Electr. & Comput. Eng., Victoria Univ., BC, Canada

Volume

44

Issue

7

fYear

1997

fDate

7/1/1997 12:00:00 AM

Firstpage

650

Lastpage

655

Abstract

In this brief we present a method for the weighted low-rank approximation of general complex matrices along with an algorithmic development for its computation. The method developed can be viewed as an extension of the conventional singular value decomposition to include a nontrivial weighting matrix in the approximation error measure. It is shown that the optimal rank-K weighted approximation can be achieved by computing K generalized Schmidt pairs and an iterative algorithm is presented to compute them. Application of the proposed algorithm to the design of FIR two-dimensional (2-D) digital filters is described to demonstrate the usefulness of the algorithm proposed

Keywords

FIR filters; approximation theory; frequency response; iterative methods; network synthesis; singular value decomposition; two-dimensional digital filters; 1D transfer functions; 2-D digital filter design; 2D FIR filters; algorithmic development; amplitude response; approximation error measure; general complex matrices; generalized Schmidt pairs; iterative algorithm; nontrivial weighting matrix; numerical linear algebra; optimal rank-K weighted approximation; singular value decomposition; weighted low-rank approximation; Approximation algorithms; Digital filters; Finite impulse response filter; Frequency response; Iterative algorithms; Linear algebra; Matrix decomposition; Signal processing algorithms; Singular value decomposition; Two dimensional displays;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.596949

Filename

596949