An Efficient Algorithm for the Optimization of FIR Filters Synthesized Using the Multistage Frequency-Response Masking Approach

Abstract

A very efficient technique to drastically reduce the number of multipliers and adders in narrow transition-band linear-phase finite-impulse response digital filters is to use the one-stage or multistage frequency-response masking (FRM) approach originally introduced by Y.C. Lim (see ibid.,1986). In the original synthesis techniques developed by Lim and Lian (see ibid.,1993), the subfilters in the overall implementation are separately designed. As shown earlier by the first two authors of this contribution as well as Johansson, the arithmetic complexity in the one-stage FRM filter designs can be considerably reduced by using the following two-stage technique for simultaneously optimizing all subfilters. First, a suboptimal solution is found by using a simple design scheme. Second, this solution is used as a start-up solution for further optimization being carried out by an efficient unconstrained nonlinear optimization algorithm. This paper exploits this approach for synthesizing multistage FRM filters. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized FRM filters are approximately 70 percent compared with those of the filters synthesized using the original multistage FRM filter design schemes.