Design of 2-D FIR filters with real and complex coefficients using two approximation criteria

In the paper, a method for designing two-dimensional finite impulse response linear phase digital filters is presented. The method can be applied for designing filters with both real and complex impulse response. In the method, two approximation criteria are used, i.e., the equiripple error criterion in the passband and the least-squared (LS) error criterion in the stopband. The design problem is solved by means of its transformation into an equivalent bicriterion optimization problem. A column vector Y of filter coefficients is defined and two objective functions X-1 (Y) and X-2(Y) are introduced. The function X, (Y) has the global minimum equal to zero when the amplitude error is equiripple in the passband. The LS error in the stopband is used as the second objective function X-2(Y). The bicriterion optimization problem is converted into a single criterion one using the weighted sum strategy. Optionally, a constraint on the maximum permissible error in the passband can also be added and easily incorporated into the optimization problem. The obtained constrained minimization problem is solved using the penalty function algorithm. Unconstrained minimization is performed by means of a conjugate gradient method. Three design examples illustrating the application of the proposed method are given. The results are compared with those obtained using the equiripple and the LS approaches.