Singer, . “Signal Processing and Communication with Solitons” Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton: CRC Press LLC, 1999 c 1999 by CRC Press LLC .75 Signal Processing and Communication with Solitons Introduction Soliton Systems: The Toda Lattice The Inverse Scattering Transform New Electrical Analogs for Soliton Systems Communication with Soliton Signals Low Energy Signaling Toda Circuit Model of Hirota and Suzuki • Diode Ladder Circuit Model for Toda Lattice • Circuit Model for Discrete-KdV Noise Dynamics in Soliton Systems Estimation of Soliton SiAs we increasingly turn to nonlinear models to capture some of the more salient. | Singer . Signal Processing and Communication with Solitons Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 75 Signal Processing and Communication with Solitons Andrew C. Singer Sanders A Lockheed Martin Company Introduction Soliton Systems The Toda Lattice The Inverse Scattering Transform New Electrical Analogs for Soliton Systems Toda Circuit Model of Hirota and Suzuki Diode Ladder Circuit Model for Toda Lattice Circuit Model for Discrete-KdV Communication with Soliton Signals Low Energy Signaling Noise Dynamics in Soliton Systems Toda Lattice Small Signal Model Noise Correlation Inverse Scattering-Based Noise Modeling Estimation of Soliton Signals Single Soliton Parameter Estimation Bounds Multi-Soliton Parameter Estimation Bounds Estimation Algorithms Position Estimation Estimation Based on Inverse Scattering Detection of Soliton Signals Simulations References Introduction As we increasingly turn to nonlinear models to capture some of the more salient behavior of physical or natural systems that cannot be expressed by linear means systems that support solitons may be a natural class to explore because they share many of the properties that make LTI systems attractive from an engineering standpoint. Although nonlinear these systems are solvable through inverse scattering a technique analogous to the Fourier transform for linear systems 1 . Solitons are eigenfunctions of these systems which satisfy a nonlinear form of superposition. We can therefore decompose complex solutions in terms of a class of signals with simple dynamical structure. Solitons have been observed in a variety ofnatural phenomena from water and plasma waves 7 12 to crystal lattice vibrations 2 and energy transport in proteins 7 . Solitons can also be found in a number of man-made media including super-conducting transmission lines 11 and nonlinear circuits 6 13 . .
