Design of linear phase FIR digital filters using minimal number of adders and subtractors

Linear phase FIR digital filters whose coefficients are expressed as canonic signed digit (CSD) code can be efficiently realized by using a small number of adders and subtractors instead of multipliers. Common uses of the adders and subtractors can further reduce the number of adders and subtractors (NAS). The use of additional adders and subtractors to recover the reduction can improve the frequency responses of those filters. An algorithm to optimize the frequency responses of such filters is proposed. Many examples confirm that, using the specified NAS, the obtained filters leave better frequency responses compared to the conventional CSD structures.