An analytical approach for obtaining a closed-form solution to theleast-square design problem of 2-D zero-phase FIR filters

摘要

A closed-form least-square solution to the design problem ofngeneral two-dimensional (2-D) real zero-phase FIR filters is obtained.nAn in-depth study of the functions and matrices arising from the problemndefinition reveals some very useful structural properties. It is shownnthat these properties lead to an optimal analytical solution for thenfilter coefficients, making it unnecessary to use design proceduresninvolving optimization techniques or matrix inversion operations. Thenderived closed-form expressions for filter coefficients allow theirnevaluation directly from the filter's frequency response specifications,nresulting in a greatly reduced computational complexity. It is confirmednthrough design examples that the proposed technique enjoys a very shortndesign time and it rises very slowly as the filter order is increased