A new eigenfilter based on total least squares error criterion

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.