An efficient matrix-based algorithm for the WLS design of 2-D FIR filters with centrally symmetric or antisymmetric response

A new matrix-based algorithm is presented for the weighted least squares (WLS) design problem of two-dimensional (2-D) finite impulse response (FIR) filters with centrally (anti)symmetric response. Firstly, the optimality condition of such optimization problem is obtained and expressed as a pair of matrix equations involving two matrix variables. Then, by introducing a parameter, we develop a matrix-based iterative algorithm to solve the optimality condition equations. Further, the convergence of the algorithm is established by using linear operators theory. Because matrix iterative operations are used and the coefficients of filters are in their natural matrix forms, great savings in computations and memory space required are achieved. Finally, a design example and comparisons to existing methods are provided to illustrate the effectiveness and efficiency of the proposed algorithm.