Design of efficient FIR filters using cyclotomic polynomial prefilters

The authors present an efficient FIR (finite impulse response) filter design algorithm that generalizes existing cascaded FIR prefilter-equalizer methods. They propose using cyclotomic polynomial building blocks to form a multiplierless prefilter with impressive stopband performance, and provide a straightforward strategy for choosing the polynomials to match the filter specifications. A uniformly space equalizer is optimally (L_∞) designed via a modified Parks-McClellan algorithm, or a more efficient, nonuniformly spaced equalizer is optimally (weighted L₂) designed using complex basis function subset selection methods. These techniques, which can be applied to a broad class of filter design problems, typically provide a 35-85% reduction in the number of additions and multiplications required, with a cost of 10-45% additional delays