DSPA-2000, V1, pp.166-169. VARIATION OF INITIAL PARAMETERS IN DESIGN FIR DIGITAL FILTERS WITH FINITE WORDLENGTH COEFFICIENTS

Abstract. A method based on the variation of initial parameters is extend on the finite wordlength coefficient design of FIR digital filters. Their efficiency is confirmed on particular examples of the filter design with minimum of the total number of adders in multiplierless structures or with optimal magnitude responses in a minimax sense at the given coefficient wordlength. The small dimension of optimization problems, which is not dependent on a transfer function order, and the independence of the base algorithm from an objective function kind involve attention to the use of the variation of initial parameters (VIP) in the finite wordlength coefficient design of FIR digital filters. The efficiency of VIP algorithms was confirmed on design examples of cascade IIR filters [1-3] and filters based on parallel connection of two allpass networks [4]. Opportunities of VIP in design problems of FIR digital filters were actually not investigated. So, in [5] VIP technique only for minimization of the statistical coefficient wordlength was applied, and in [6] negative results on its using for the design with the given real coefficient wordlength were obtained. In this paper is shown that VIP technique gives excellent results in respect to the FIR linear phase digital filter design both with minimum of the total number of adders in multiplierless structures and with optimal magnitude responses in a minimax sense at the given coefficient wordlength. VIP method in design FIR digital filters. We shall present the coefficient vector of FIR filters h= ( ) as some vector-function of an initial parameter vector p, i.e. h h hN0 1, ,..., −1 h=F(p). We use a method of weighing [7] to definition h. In this case the kind of the function will depend on the type of an ideal filter and on the used weight function ( window). It is possible to show that for the filters with standard requirements at N=const the vector of parameters i