A new iterative reweighted least squares algorithm for the design of FIR filters

It is known that iterative reweighted least squares (IRLS) algorithms are efficient techniques for the design of digital filters. The main computational load in IRLS algorithms is to solve a series of weighted least squares (WLS) subproblems, which usually needs the time-consuming evaluation of matrix inversion. This paper presents a new and very efficient IRLS algorithm, in which a simple iterative procedure is developed for solving those WLS subproblems. It is verified that the iterative procedure is guaranteed to converge and is computationally more efficient than using matrix inversion. Thus, the design efficiency is improved greatly, especially for high-order filters. Design examples and comparisons to some existing algorithms are given to show the excellent performance of the proposed algorithm.