Recursive digital filter design via covariance sequence approximation

In this paper we propose a modified solution to the general nonlinear least-squares approximation problem for digital filter design. We choose to approximate the covariance sequence associated with an ideal filter because it arises more naturally in spectrum matching problems than does the unit pulse response sequence. The design procedure resulting from our approach requires the rooting of an nth-order polynomial, the solution of an nth-order system of linear equations, and the calculation of a (2n - 1)-point DFT for the design of an ARMA (2n, 2(n - 1)) digital filter.