Periodic behaviors in a digital filter with two´s complement arithmetic

It is well known that the second-order digital filter with two´s complement arithmetic may exhibit chaotic behaviors. It is also known that for certain class of filter parameters, the second-order filter exhibits periodic behaviors. This paper studies the relation between the period of periodic trajectories and the period of trajectory traveling patterns for the particular class of filter parameters. A complete classification of periodic behaviors is given and the underlying relations are fully explored. The shape and layout of the regions in the state space displaying periodic behavior of the same type are fully examined, The mathematical analysis is accompanied by considerable simulation results