A CLOSED-FORM SOLUTION TO THE LEAST-SQUARE DESIGN PROBLEM OF 2-D LINEAR-PHASE FIR FILTERS

In this paper, the least-square design problem of a general two dimens ional (2-D) linear-phase FIR filter with an arbitrary magnitude respon se is studied, By minimizing the frequency-domain error function and e xploiting some of the properties of the functions and matrices associa ted with the design problem, a novel closed-form solution is developed , The solution is expressed in terms of the desired magnitude specific ations and is eventually presented as an explicit expression for the i mpulse response of the filter to be designed, making a very fast evalu ation of the filter's coefficients possible, It is also shown that whe n this solution is used to design filters that have centrosymmetric an d quadrantally symmetric magnitude responses, some further computation al savings can be achieved, Several design examples illustrating the e ffectiveness of the proposed solution are considered.