Method and apparatus for communication with chaotic and other waveforms

Abstract

A method and apparatus for communicating with chaotic and other waveforms employs a filter for estimating a parameter that describes a property of a signal. The filter is constructed by defining a system that models the source of the signal. The system is partitioned into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term that makes the second subsystem stable and synchronizable with the signal. The signal is introduced as input to the second subsystem and an element of the second subsystem is substituted into a corresponding element of the first subsystem, thereby generating a signal-activated subsystem. An integration factor is introduced to the signal-activated subsystem to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time. The signal-activated subsystem is integrated with respect to time with the integration factor, generating an equation of integrals in which the parameter is brought out of any of the integrals containing the parameter. The equation of integrals is solved for the parameter so that a multiple of the parameter is expressed as a combination of integrals, which is applied to a low-pass filter to inhibit any singularities in the combination of integrals, thereby generating a filtered combination of integrals. A circuit is constructed from a plurality of circuit elements, each circuit element being an analog of an integral of the filtered combination of integrals.

Dependencies are inferred from the claim text.