Towards optimal least square filters using the eigenfilter approach

In this paper, we propose a new eigenfilter approach to designing least square error filters. The filters are obtained by finding an eigenvector of a real, symmetric and positive definite matrix, which is numerically stable. The proposed algorithm has two advantages. First, we show that the least-square solution, which can only be obtained through matrix inversion in the literature, can be asymptotically reached with our algorithm. Second, when numerical errors break. the matrix inversion method, our algorithm can still find some ìoptimalî filter through tuning an internal parameter.