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

This paper salves the weighted least mean square (WLMS) design of two- dimensional (2-D) finite impulse response (FIR) filters viith general half plane symmetric frequency responses and nonnegative weighting fun ctions, Tile optimal solution is characterized by a pair of coupled in tegral equations, and the existence and uniqueness of the WLMS solutio n for 2-D FIR filter design ape established, Two efficient numerical a lgorithms using a 2-D fast Fourier transform (FFT) are proposed to sol ve the WLMS solution, One is based on the contraction mapping and fix point theorem characterizing the coupled integral equation; the other uses conjugate gradient techniques, which guarantees finite convergenc e, The associated computational complexity is analyzed and compared wi th existing algorithms, Examples are used to illustrate the effectiven ess of the proposed design algorithms. The selection of weighting func tions to improve the minimax performance of the filter is also discuss ed.