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Symbolic Sequences Generated by a Special Class of Discrete Systems With Discontinuity and Input

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Abstract

In this paper, we study the symbolic sequences generated by aclass of discrete systems. This class contains the doubleΣΔ-modulators, a typical example of discretetime electronic systems with discontinuity and input. First we develop ageneral theory and then we apply it to some examples in order to obtainsets of inadmissible sequences.

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References

  1. Galias, Z. and Ogorzalek, M., 'On symbolic dynamics of a chaotic second-order digital filter', International Journal of Circuit Theory and Applications 20, 1992, 401-409.

    Google Scholar 

  2. Chua, L. O. and Lin, T., 'Fractal patter of second order non-linear digital filters: A new symbolic analysis', International Journal of Circuit Theory and Applications 18, 1990, 541-550.

    Google Scholar 

  3. Chua, L. O. and Lin, T., 'Chaos and fractals from third-order digital filters', International Journal of Circuit Theory and Applications 18, 1990, 241-255.

    Google Scholar 

  4. Chua, L. O. and Lin, T., 'Chaos in digital filters', IEEE Transactions on Circuits and Systems 35(6), 1988, 648-658.

    Google Scholar 

  5. Wu, C. W. and Lin, T., 'Symbolic dynamics of piecewise linear maps', IEEE Transactions on Circuits and Systems 41(6), 1994, 420-424.

    Google Scholar 

  6. Feely, O. and Chua, L. O., 'The effect of integrator leak in 61 modulation', IEEE Transactions on Circuits and Systems 38(11), 1991, 1293-1305.

    Google Scholar 

  7. Feely, O., 'Non-linear dynamics of chaotic double-loop ∑ — Δ modulation', in Proceedings of IEEE International Symposium on Circuits and Systems, London, IEEE, New York, 1994, pp. 101-104.

    Google Scholar 

  8. Kotsios, S. and Feely, O., 'The model matching problem for 61 modulators', IMA Journal of Mathematical Control and Information 15, 1998, 93-104.

    Google Scholar 

  9. Kotsios, S. and Feely, O., 'Some results on dynamics of special double-loop 61 modulators', Nonlinear Dynamics 13(1), 1997, 83-98.

    Google Scholar 

  10. Pinault, S. C. and Lopresti P. V., 'On the behaviour of the double-loop Sigma-Delta modulator', IEEE Transactions on Circuits and Systems 40(8), 1993, 467-479.

    Google Scholar 

  11. Wang, H., 'A geometric view of 61 modulations', IEEE Transactions on Circuits and Systems 39(6), 1992, 402-405.

    Google Scholar 

  12. Wu, C. W. and Lin, T., 'Properties of admissible symbolic sequences in a second-order digital filter with overflow nonlinearity', International Journal of Circuit Theory and Applications 21, 1993, 299-307.

    Google Scholar 

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Kotsios, S. Symbolic Sequences Generated by a Special Class of Discrete Systems With Discontinuity and Input. Nonlinear Dynamics 22, 165–181 (2000). https://doi.org/10.1023/A:1008378529170

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  • DOI: https://doi.org/10.1023/A:1008378529170

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