A Bi-matrix-based Conjugate Gradient Algorithm for the WLS Design of Centro-symmetric 2-D FIR Filters

The weighted least squares (WLS) design problem of centro-symmetric two-dimensional (2-D) FIR filters is investigated in this paper. Firstly, the optimality condition of the design problem is expressed as a linear operator equation in two matrix variables containing the filter design coefficients. Then by properly defining an inner product on the solution space, a bi-matrix-based conjugate gradient algorithm is obtained to solve the linear operator equation. The proposed design algorithm is shown to converge in the finite steps. An illustrative design example is given to show that the proposed algorithm consumes much less design time and has the higher design accuracy than that by some existing methods.