ON THE USE OF CYCLOTOMIC POLYNOMIAL PREFILTERS FOR EFFICIENT FIR FILTER DESIGN

We present an efficient FIR filter design algorithm that generalizes e xisting cascaded FIR prefilter-equalizer methods. We propose using cyc lotomic polynomial ''building blocks'' to form a multiplierless prefil ter with impressive stopband performance, and we provide a straightfor ward strategy for choosing the polynomials to match filter specificati ons. We then provide two options for design of the equalizer. A unifor mly spaced equalizer can be optimally (L(infinity)) designed via a mod ified Parks-McClellan algorithm. However, we also propose a new algori thm, based on complex basis function subset selection methods, to opti mally design a more efficient, nonuniformly spaced equalizer. Our tech niques, which can be applied to a broad class of filter design problem s, typically provide a 35%-85% reduction in the number of additions an d multiplications required, with a cost of 10%-45% additional delays. Furthermore, our methods provide reduced coefficient quantization sens itivity and reduced roundoff noise.