1. Chaotic Oscillations in Dissipative and Second-Order Direct-Form II Digital Filters with a 2's Complement Adder.
- Author
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Kawamata, Masayuki, Sasaki, Shinji, and Higuchi, Tatsuo
- Subjects
- *
CHAOS theory , *DIGITAL filters (Mathematics) , *LOCUS (Mathematics) , *ATTRACTORS (Mathematics) , *DIFFERENTIABLE dynamical systems , *MATHEMATICS - Abstract
This paper studies the chaotic oscillations in a dissipative system generated by a second-order direct-form II digital filter with a 2's complement adder. The locus of this chaotic oscillation is absorbed into the parallel lines comprising the Cantor-like set on the state space. In this paper, with respect to the chaotic oscillation, the initial value dependence of the locus, the output distribution, and the fractal dimensions of the locus on the state space are investigated as the fundamental nature of the chaos. Also, by considering this filter as the two-dimensional mapping, the mechanism generating the Cantor-like attractor is studied. From this study, it is shown that the 2's complement adder characteristic has functions for stretching and folding of the state space causing the chaos. Also, the coefficient dependence of the Cantor-like attractor is studied and the relationship between the fractal dimensions of the locus and the coefficient are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1995
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