Cyclotomic polynomial filters based on cascaded recursive building blocks with minimum number of additions

The design of low-complexity filters based on the first 104 Cyclotomic Polynomials (CPs) has received great interest because CPs have coefficients belonging to the set {-1, 0, 1}, thus yielding simple and efficient multiplierless structures. Recently, the design of CP filters has been extended in a search space containing the first 200 CPs and it has been shown that their recursive z-transfer functions still have coefficients in the set {-1, 0, 1}, resulting in complexity reductions especially for narrow passband filters. In this paper, it is shown that any filter with arbitrarily narrow passband can be designed regardless of the CP´s indexes such that the resulting cascade of recursive building blocks has minimum number of additions.