On the Use of Cyclotomic Polynomial Prefilters for Efficient FIR Filter Design

We present an efficient FIR filter design algorithm that generalizes existing cascaded FIR prefilter-equalizer methods. We propose using cyclotomic polynomial “building blocks” to form a multiplierless prefilter with impressive stopband performance, and we provide a straightforward strategy for choosing the polynomials to match filter specifications. We then provide two options for design of the equalizer. A uniformly spaced equalizer can be optimally (L«) designed via a modified Parks-McClellan algorithm. However, we also propose a new algorithm, based on complex basis function subset selection methods, to optimally design a more efficient, nonuniformly spaced equalizer. Our 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. Furthermore, our methods provide reduced coefficient quantization sensitivity and reduced roundoff noise. © 1993 IEE