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.