On the use of cyclotomic polynomial prefilters for efficient FIR filter design

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 they provide a straightforward strategy for choosing the polynomials to match filter specification. Two options for design of the equalizer are provided. A uniformly spaced equalizer can be optimally (L_∞) designed via a modified Parks-McClellan algorithm. A new algorithm, based on complex basis function subset selection methods, is also proposed for optimal design of a more efficient, nonuniformly spaced equalizer. The 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. The methods also provide reduced coefficient quantization sensitivity and reduced roundoff noise