WEIGHTED LEAST MEAN-SQUARE DESIGN OF 2-D FIR DIGITAL-FILTERS

This paper is concerned with weighted least mean square design of two dimensional (2-D) zero-phase FIR filters with quadrantally symmetric a nd antisymmetric frequency responses. The optimal solutions are first characterized by certain integral equations, and the existence, and un iqueness of the weighted least mean square solution for 2-D FIR filter design are then established using contraction mapping, and fixed poin t theorem [13]. Explicit solution in closed form for discretized weigh ted least mean square error is obtained for 2-D zero-phase FIR filters , which can be considered as an extension of [15], [1]. Further, two n umerical algorithms are proposed to iteratively solve the weighted lea st mean square solution. Convergence of the iterative algorithms is es tablished, and estimates of the convergence rate are also derived. Exa mples are used to illustrate the effectiveness of the proposed design algorithms.