A least-square method for the design of 2-D FIR digital filters with arbitrary frequency responses

In this paper, the least-square design problem of 2-D FIR digital filters with arbitrary frequency responses is investigated. By exposing and exploiting some of the characteristics of the complex matrices associated with the approximation problem, a closed-form solution is developed. The solution is presented as an explicit expression for the impulse response corresponding to the desired frequency response specifications. Thus, the method avoids the usual time-consuming procedures of optimization or matrix inversion and makes an extremely fast calculation of the filter´s coefficients possible. It is also shown that when this solution is used to design some specific classes of filters, further computational savings can be achieved. Design examples for both linear-phase and nonlinear-phase filters are considered