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Complex orbits in a second-order digital filter with sinusoidal response

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  • Yuan, Li-Guo
  • Nie, Du-Xian
  • Fu, Xin-Chu

Abstract

This paper analyzes a two-dimensional piecewise affine map driven by a periodic perturbation, which is relevant to the second-order digital filters with sinusoidal response. By using symbolic dynamics method, a formula for an arbitrary iterate of the map is derived. When overflow occurs, the system is nonlinear. If the corresponding symbolic sequences are aperiodic, some orbits are computed and illustrated. These show that the orbit structure is much richer than that of the autonomous and step-response cases. And numerical experiments to estimate the fractal dimension of the chaotic cases are performed with fractal Brownian motion. Finally, higher order periodic trajectories are found via the particle swarm optimization.

Suggested Citation

  • Yuan, Li-Guo & Nie, Du-Xian & Fu, Xin-Chu, 2009. "Complex orbits in a second-order digital filter with sinusoidal response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1660-1667.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1660-1667
    DOI: 10.1016/j.chaos.2007.09.048
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    References listed on IDEAS

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    1. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    2. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
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