WLS design of centro-symmetric 2-D FIR filters using matrix iterative algorithm

The weighted least squares (WLS) design problem of two-dimensional (2-D) FIR filters with centro-symmetric response is considered in this paper. Its optimality condition is given and expressed as a pair of matrix equations, which involves two matrix variables, i.e., the coefficients of filters to be determined. Then, based on the optimality condition, a matrix iterative algorithm is developed to solve the design problem and its convergence is established using linear operator theory. Because the coefficients of filters are in their natural matrix forms in the algorithm, great savings in computations and memory space required are achieved. Finally, a design example and comparisons with existing methods are provided to illustrate the effectiveness and efficiency of the proposed algorithm.