A new approach for weighted least-square design of FIR filters

In this paper, a new approach for weighted least square (WLS) design of FIR filters is presented, in which an iterative procedure is developed for the inversion of the matrix involved in the design. By imposing a mild constraint on the update factor of the weighting function, the inverse of a matrix is expanded as a convergent power series. By exploiting the properties of some of the matrices involved in the design, a modified version of the series that converges rapidly is then proposed to evaluate the inverse in each iteration. It is shown that due to the fast convergence of the power series, one has to evaluate only the first two or three terms of the series after a few initial iterations, implying that the conventional operation for matrix inversion is simplified significantly