An iterative procedure for matrix inversion in weighted least-square design of FIR filters

It has been shown by some researchers that in a problem of weighted least-square (WLS) design of an FIR filter, most of the design computation pertains to the evaluation of the inverse of a matrix in order to solve a system of equations. In this paper, a new iterative procedure is developed for the inversion of the matrices involved in the design. By expanding the inverse of a matrix as a convergent series, an updating formula for evaluating the inverse for each iteration is obtained, so that the proposed algorithm requires an inverse for only a few initial iterations but does not need any numerical operations for matrix inversion in succeeding iterations. It is also shown that the proposed iterative procedure is applicable for a wide range of weighting functions used for least-square designs.