Least-squares design of two-dimensional recursive filters with specified magnitude and linear phase

Abstract

An efficient space-domain procedure is presented for the design of two-dimensional recursive filters with specified magnitude and linear phase. The design procedure is based on both the canonical and the modified least-squares approximation techniques. The nonlinear equations obtained in the canonical least-squares approximation are efficiently solved by the one- dimensional Gauss—Newton optimization method, after the two-dimensional data are lexico- graphically ordered. The gradient and the Hessian matrix, needed in the solution, are calculated recursively. Initial values of the parameters are obtained from the linear modified least-squares (MLS) approximation. To illustrate the efficiency of the proposed design procedure, the design of fan and circularly symmetric filters are given.