A weighted L2 based method for the design of arbitrary one dimensional FIR digital filters

FIR filters obtained with classical L₂ methods have performance that is very sensitive to the form of the ideal response selected for the transition region. This is because, usually, filter specifications do not constrain in any way the ideal frequency response inside this region. In this paper we propose a new general method for the weighted L₂ 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.