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71 Chaotic Signals and Signal Processing

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Signals generated by chaotic systems represent a potentially rich class of signals both for detecting and characterizing physical phenomena and in synthesizing new classes of signals for communications, remote sensing, and a variety of other signal processing applications. | Oppenheim A.V. Cuomo K.M. Chaotic Signals and Signal Processing Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 71 Chaotic Signals and Signal Processing Alan V. Oppenheim Massachusetts Institute of Technology Kevin M. Cuomo MIT Lincoln Laboratory 71.1 Introduction 71.2 Modeling and Representation of Chaotic Signals 71.3 Estimation and Detection 71.4 Use of Chaotic Signals in Communications Self-Synchronization and Asymptotic Stability Robustness and Signal Recovery in the Lorenz System Circuit Implementation and Experiments 71.5 Synthesizing Self-Synchronizing Chaotic Systems References 71.1 Introduction Signals generated by chaotic systems represent a potentially rich class of signals both for detecting and characterizing physical phenomena and in synthesizing new classes of signals for communications remote sensing and a variety of other signal processing applications. In classical signal processing a rich set of tools has evolved for processing signals that are deterministic and predictable such as transient and periodic signals and for processing signals that are stochastic. Chaotic signals associated with the homogeneous response of certain nonlinear dynamical systems do not fall in either of these classes. While they are deterministic they are not predictable in any practical sense in that even with the generating dynamics known estimation of prior or future values from a segment of the signal or from the state at a given time is highly ill-conditioned. In many ways these signals appear to be noise-like and can of course be analyzed and processed using classical techniques for stochastic signals. However they clearly have considerably more structure than can be inferred from and exploited by traditional stochastic modeling techniques. The basic structure of chaotic signals and the mechanisms through which they are generated are described in a variety of introductory books .