AN ANALYTICAL APPROACH FOR OBTAINING A CLOSED-FORM SOLUTION TO THE LEAST-SQUARE DESIGN PROBLEM OF 2-D ZERO-PHASE FIR FILTERS

A closed-form least-square solution to the design problem of general t wo-dimensional (2-D) real zero-phase FIR filters is obtained. An in-de pth study of the functions and matrices arising from the problem defin ition reveals some very useful structural properties. It is shown that these properties lead to an optimal analytical solution for the filte r coefficients, making it unnecessary to use design procedures involvi ng optimization techniques or matrix inversion operations. The derived closed-form expressions for filter coefficients allow their evaluatio n directly from the filter's frequency response specifications, result ing in a greatly reduced computational complexity. It is confirmed thr ough design examples that the proposed technique enjoys a very short d esign time and it rises very slowly as the filter order is increased.