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

Author

Yu, Xinghuo ; Galias, Zbigniew

Author_Institution

Fac. of Inf. & Commun., Central Queensland Univ., Rockhampton, Qld., Australia

Volume

48

Issue

10

fYear

2001

fDate

10/1/2001 12:00:00 AM

Firstpage

1177

Lastpage

1190

Abstract

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

Keywords

chaos; digital arithmetic; digital filters; filtering theory; digital filter; filter parameters; periodic behaviour; periodic trajectories; second-order filter; trajectory traveling patterns; two´s complement arithmetic; Analytical models; Chaotic communication; Circuit simulation; Computational modeling; Digital arithmetic; Digital filters; Filtering; Mathematical analysis; Shape; State-space methods;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.956012

Filename

956012