An L2 based method for the design of one dimensional FIR digital filters

FIR filters obtained with the classical L₂ method have performance that is very sensitive to the form of the ideal response selected for the transition region. In this paper we propose a means for selecting the unknown part of a complex ideal response optimally. By selecting a proper L₂ criterion and using variational techniques we succeed in minimizing the criterion with respect to the ideal response and thus obtain its corresponding optimum form. The complete solution to the problem can be obtained by solving a simple system of linear equations suggesting a reduced complexity for the proposed method. Using the optimum form of the ideal response we also propose a new suboptimal method for the design of weighted FIR filters. Design examples are presented to illustrate the performance of the proposed method