Design of FIR filters with equiripple passband and least-squares stopband

In some applications, it is necessary to minimize the maximum amplitude error in the passband and to minimize the total stopband energy. In some cases, both total stopband energy and the maximum stopband gain should be considered. In this paper, a new approach for the design of low-pass linear phase FIR filters with the equiripple passband and the least-squares stopband is proposed. In this approach, the design problem is solved by means of its transformation into an equivalent bicriterion optimization problem. In order to do this, the filter coefficients vector Y is defined and two objective functions X1(Y) and X2(Y) are introduced. The conditions on the maximum permissible error in the passband or in the stopband can be optionally imposed as extra constraints. Two design examples demonstrating the usefulness of the proposed approach are given.