Title :
Arnold tongues and devil´s staircase in a digital filter employing saturation arithmetic
Author :
Ogorzalek, Maciej J. ; Galias, Zbigniew
Author_Institution :
Dept. of Electr. Eng., Acad. of Min. & Metall., Krakow, Poland
Abstract :
The authors analyse the dynamic behaviors encountered in a digital filter employing a saturation-type adder overflow characteristic. The influence of changes of filter parameters on its dynamics is studied in detail. A two-parameter bifurcation diagram has been constructed, revealing an extremely rich and complex structure of Arnold tongues in the parameter space. These tongues are composed of a sequence of self-similar, `sausage-like´ regions. In one-parameter analyses, devil´s staircase changes of winding numbers of encountered orbits can be observed. Mathematical considerations show that the tongues do not overlap and the system cannot exhibit chaotic behavior. However, it is possible to find oscillations with any arbitrarily chosen period
Keywords :
digital filters; stability; Arnold tongues; complex structure; devil´s staircase; dynamic behaviors; encountered orbits; oscillations; saturation arithmetic; saturation-type adder overflow characteristic; two-parameter bifurcation diagram; winding numbers; Adders; Bifurcation; Chaos; Digital arithmetic; Digital filters; Equations; Nonlinear dynamical systems; Orbits; Stability; Tongue;
Conference_Titel :
Circuits and Systems, 1991., IEEE International Sympoisum on
Print_ISBN :
0-7803-0050-5
DOI :
10.1109/ISCAS.1991.176354