Advertisement

Nonlinear Dynamics from Infinite Impulse Response Matched Filters

  • Ned J. CorronEmail author
  • Jonathan N. Blakely
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)

Abstract

Standard methods of communication theory are used to derive optimal waveforms for transmitting information through noise using infinite impulse response matched filters as receivers. In two examples, the derived optimal communication waveforms are chaotic. Extrapolating from these simple examples, we posit that the optimal communication waveform for any stable infinite impulse response filter can similarly be chaotic. This conjecture implies the phenomena of nonlinear dynamics and chaos are fundamental and essential to a full understanding of modern communication theory.

Keywords

Matched Filter Infinite Impulse Response Linear Filter Positive Lyapunov Exponent Chaotic Nature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    M.B. Pursley, Introduction to Digital Communications (Prentice Hall, Upper Saddle River, 2005)Google Scholar
  2. 2.
    G. Turin, An introduction to matched filters. IRE Trans. Inf. Theory 6, 311–329 (1960)MathSciNetCrossRefGoogle Scholar
  3. 3.
    N.J. Corron, J.N. Blakely, Chaos in optimal communication waveforms. Proc. R. Soc. A 471, 2015022 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    S.T. Hayes, Chaos from linear systems: Implications for communicating with chaos, and the nature of determinism and randomness. J. Phys. Conf. Ser. 23, 215–237 (2005)CrossRefGoogle Scholar
  5. 5.
    Y. Hirata, K. Judd, Constructing dynamical systems with specified symbolic dynamics. Chaos 15, 033102 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    N.J. Corron, S.T. Hayes, S.D. Pethel, J.N. Blakely, Chaos without nonlinear dynamics. Phys. Rev. Lett. 97, 024101 (2006)CrossRefGoogle Scholar
  7. 7.
    N.J. Corron, S.T. Hayes, S.D. Pethel, J.N. Blakely, Synthesizing folded band chaos. Phys. Rev. E 75, 045201 (2007)Google Scholar
  8. 8.
    N.J. Corron, J.N. Blakely, M.T. Stahl, A matched filter for chaos. Chaos 20, 023123 (2010)CrossRefzbMATHGoogle Scholar
  9. 9.
    T.Y. Li, J.A. Yorke, Period three implies chaos. Am. Math. Mon. 82, 985–992 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Charles M. Bowden LaboratoryU.S. Army AMRDECHuntsvilleUSA

Personalised recommendations