Synthesis of recursive digital filters by state feedback of non‐recursive cascaded lattice filters

Abstract

AbstractA general method to realize any digital transfer function is presented. The method is understood as a two‐stage process. First, a non‐recursive system having the same transfer zeros as the given transfer function is synthesized in the form of a special cascaded lattice structure. Then the poles of the non‐recursive system, which occur exclusively at the origin, are shifted by extending this system through state feedback so that the shifted poles coincide with the poles of the specified transfer function while the transfer zeros remain unchanged.1 Compared with the well‐known cascaded lattice structures proposed by Mitra et al.2 the resulting filters exhibit advantages in the realization of the adders. Furthermore, it is pointed out how the cascaded lattice structure2 can be derived from the structure introduced here by applying a state transformation.