Weighted Least Mean Square Design of Two-dimensional FIR Digital Filters

This paper is concerned with weighted least mean square design of two-dimensional (2-D) zero-phase FIR lters with quadrantally symmetric and antisymmetric frequency responses. The optimal solutions are rst characterized by certain integral equations, and the existence, and uniqueness of the weighted least mean square solution for 2-D FIR lter design are then established using contraction mapping, and xed point theorem 13]. Explicit solution in closed form for discretized weighted least mean square error is obtained for 2-D zero-phase FIR lters which can be considered as an extension of 15, 1]. Further, two numerical algorithms are proposed to iteratively solve the weighted least mean square solution. Convergence of the iterative algorithms is established, and estimates of the convergence rate are also derived. Examples are used to illustrate the eeectiveness of the proposed design algorithms.