A new eigenfilter based on total least squares error criterion

Author

Pei, Soo-Chang ; Tseng, Chien-Cheng

Author_Institution

Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan

Volume

48

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

699

Lastpage

709

Abstract

In this paper, a new eigenfilter based on total least squares error criterion is investigated. The filter coefficients are obtained from the elements of the eigenvector corresponding to minimum eigenvalue of a real, symmetric and positive definite matrix. Four features of the new method are given. First, the computation of filter coefficients of the new eigenfilter is more numerically stable than that of the least-squares method whose solution is obtained by solving matrix inverse. Second, the new eigenfilter does not need a reference frequency point for normalization as done in traditional eigenfilter. Third, the solution of the new eigenfilter is closer to the solution of the least-squares method than that of the conventional eigenfilter. Fourth, the proposed method is easy to incorporate with linear constraints and can be extended to design equiripple and two dimensional linear phase filters. Several design examples are used to illustrate the effectiveness of this new design approach

Keywords

FIR filters; eigenvalues and eigenfunctions; equiripple filters; least squares approximations; linear phase filters; eigenfilter; equiripple; filter coefficients; linear constraints; positive definite matrix; total least squares error criterion; two dimensional linear phase; Chebyshev approximation; Computer errors; Eigenvalues and eigenfunctions; Finite impulse response filter; Frequency; Least squares methods; Linear programming; Minimax techniques; Nonlinear filters; Symmetric matrices;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.928153

Filename

928153