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On symbolic dynamics of a chaotic second‐order digital filter
Author(s) -
Galias Zbigniew,
Ogorzalek Maciej J.
Publication year - 1992
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490200406
Subject(s) - symbolic dynamics , filter (signal processing) , chaotic , modular design , fractal , computer science , digital filter , order (exchange) , dynamics (music) , theoretical computer science , algorithm , mathematics , artificial intelligence , pure mathematics , mathematical analysis , physics , finance , acoustics , economics , computer vision , operating system
Abstract This paper presents a contribution to the symbolic analysis of fractal patterns exhibited by a second‐order digital filter with modular adder overflow characteristic. We use symbolic dynamics for the analysis of phenomena encountered in the system. We present several new results concerning the existence of admissible sequences for periodic orbits in the filter. an efficient computational algorithm based on rigorous mathematical results presented in the paper enabled us to calculate sequences with long periods, thus allowing deeper understanding of the underlying mechanisms of complex behaviour encountered in the filter.