An order recursive algorithm for synthesizing linear recursive filters

The author proposes an order recursive algorithm to compute efficiently the solution to the set of linear equations for finding the parameters of a recursive filter whose unit impulse response best approximates that of the prescribed ideal response. The algorithm requires only O(p/sup 2/) operations. The inherent structure of the coefficient matrix in the system of linear equations and the inversion procedure for a partitioned matrix are used in the algorithm. In a numerical example of a low-pass filter the system of linear equations is found to be ill-conditioned. A satisfactory solution can not be achieved using the usual software routines, even with double precision, for a moderate value of the order p. The proposed algorithm is shown to be more accurate and less sensitive to this ill-conditioned case.<>