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Optimal communications with infinite impulse response matched filters

Author

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  • Milosavljevic, Marko S.
  • Corron, Ned J.
  • Blakely, Jonathan N.

Abstract

Optimal communication waveforms matched to a large and practically important class of filters are investigated and shown to be chaotic. Filters of this class are defined by an infinite impulse response (IIR) and a transfer function comprising a finite number of distinct stable poles. This class contains many of the most popular and widely used filter families, including Butterworth, Chebyshev (type I), and Bessel. For such a filter, a matched basis function is derived and convolved with a random binary sequence to construct a communication waveform. It is shown that this waveform is chaotic in the sense that it is deterministic and characterized by a positive Lyapunov exponent. This result supports a recent conjecture that optimal communication waveforms matched to stable IIR filters are chaotic, and it further establishes that chaos is fundamental to modern communication theory.

Suggested Citation

  • Milosavljevic, Marko S. & Corron, Ned J. & Blakely, Jonathan N., 2020. "Optimal communications with infinite impulse response matched filters," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920302228
    DOI: 10.1016/j.chaos.2020.109822
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    References listed on IDEAS

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    1. Werner, Frank T. & Rhea, Benjamin K. & Harrison, R. Chase & Dean, Robert N., 2017. "Electronic implementation of a practical matched filter for a chaos-based communication system," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 461-467.
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