A least-square design approach for 2-D FIR filters with arbitrary frequency response

In this paper, a least-square approach for the design of two-dimensional (2 -D) complex finite-impulse response (FIR) filters with arbitrary frequency response is presented, By minimizing the frequency-domain error function an d revealing some of the properties of the matrices associated with the desi gn problem, a closed-form solution is obtained. The solution is presented a s an expression for the impulse response corresponding to the desired frequ ency-response specification. Thus, the method avoids the usual time-consumi ng procedures of optimization or matrix inversion, and makes a very fast ca lculation of the filter's coefficients possible. It is also shown that when this solution is used to design linear-phase filters and a class of 2-D ph ase equalizers, some further computational savings can be achieved. The nov el feature of the proposed approximation approach is that it can be used to design any kind of 2-D FIR filters without employing any symmetry constrai nt on their frequency responses. Several design examples illustrating the e fficiency of the approach are considered.