A weighted L2L2-based method for the design of arbitrary one-dimensional FIR digital filters

In FIR filter design problems, filter specifications do not constrain in any way the ideal frequency response inside the transition regions. Most existing L2L2-based filter design techniques utilize this flexibility in order to improve their performance. In this paper we propose a new general method for the weighted L2L2-based design of arbitrary FIR filters. In particular, we propose a well-defined optimization criterion that depends on the selection of the desired response inside the transition regions. By optimizing our criterion we obtain desired responses that produce weighted mean square error optimum filters with extremely good characteristics. The proposed method is computationally simple since it requires the solution of a linear system of equations.