Design of FIR digital filters with very few multipliers and adders

A novel design procedure for equalizers is presented in order to yield overall multiplierless FIR (finite impulse response) filters. The technique is based on the utilization of some special equalization functions which can be efficiently implemented with only shift and addition operations like prefilters. If such a prefilter-plus-equalizer FIR filter does not meet the desired specifications, the SSS (simple symmetric-sharpening) network technique may be used to overcome the difficulty. Some useful analytic results of mathematical properties of the special equalization functions are presented. The main design procedure which relates to different equalization functions is described. A simple CAD program can be used to achieve proper designs. The usefulness of the equalization functions is investigated by some design examples. Even if M+A (the number of multipliers and adders) is used as a complexity measure for FIR digital filters, the proposed design approach also shows better performance compared to the optimal or A-W designs. It is noted that the FIR filter structures result in almost no coefficient quantization effects and can be constructed by using very simple processing elements