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

In this paper, a least-square approach for the design of two-dimensional (2D) complex finite-impulse response (FIR) filters with arbitrary frequency response is presented. By minimizing the frequency-domain error function and revealing some of the properties of the matrices associated with the design problem, a closed-form solution is obtained. The solution is presented as an expression for the impulse response corresponding to the desired frequency-response specification. Thus, the method avoids the usual time-consuming procedures of optimization or matrix inversion, and makes a very fast calculation 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 2D phase equalizers, some further computational savings can be achieved. The novel feature of the proposed approximation approach is that it can be used to design any kind of 2D FIR filters without employing any symmetry constraint on their frequency responses. Several design examples illustrating the efficiency of the approach are considered.