Additional properties of one-dimensional limit cycles

Limit cycles due to product rounding in a fixed-point implementation of a second-order recursive digital filter are examined. Some new properties deriving from Jackson¿s `effective-value¿ model are first presented. Then two limit cycle classifications are introduced based upon the notion of `reverse limit cycles¿ and `phaseplane symmetry¿. These classifications are subsequently shown to be linked to well-known results on limit cycle amplitude bounds and accessibility.