Weighted least mean square design of 2-D FIR digital filters: general weighting function

Gu and Aravena obtained weighted least mean square solutions, to the design, of 2D FIR filters, which are most suitable for quadrantally symmetric, and quadrantally antisymmetric filters with zero/one weighting functions. The present paper solves the weighted least mean square design of 2D FIR filters with general half plane symmetric frequency responses and weightings. The optimal solution is shown to be the fix point of a map characterized by a pair of coupled integral equations. An efficient numerical algorithm using a 2D FFT is proposed to iteratively solve the weighted least mean square solution. Convergence of the iterative algorithms follows from the fact that the integral equations define a contraction mapping. Examples are used to illustrate the effectiveness of the proposed design algorithms