An order recursive algorithm for synthesizing linear recursive filters
Yang Sun · International Conference on Acoustics, Speech, and Signal Processing · 2003
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.>