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.