Field-programmable analog array (FPAA) based four-state adaptive oscillator for analog frequency analysis.

Adaptive oscillators are a subset of nonlinear oscillators that can learn and encode information in dynamic states. By appending additional states onto a classical Hopf oscillator, a four-state adaptive oscillator is created that can learn both the frequency and amplitude of an external forcing frequency. Analog circuit implementations of nonlinear differential systems are usually achieved by using operational amplifier-based integrator networks, in which redesign procedures of the system topology is time consuming.

A four-state adaptive Hopf oscillator.

Adaptive oscillators (AOs) are nonlinear oscillators with plastic states that encode information. Here, an analog implementation of a four-state adaptive oscillator, including design, fabrication, and verification through hardware measurement, is presented. The result is an oscillator that can learn the frequency and amplitude of an external stimulus over a large range.

Exact analytic solution for a chaotic hybrid dynamical system and its electronic realization.

A novel hybrid dynamical system comprising a continuous and a discrete state is introduced and shown to exhibit chaotic dynamics. The system includes an unstable first-order filter subject to asynchronous switching of a set point according to a feedback rule. Regular samples of the continuous state yield a one-dimensional return map that is a tent function.

Generating and Detecting Solvable Chaos at Radio Frequencies with Consideration to Multi-User Ranging.

High entropy waveforms exhibit desirable correlation properties in radar and sonar applications when multiple systems are used in close proximity. Unfortunately, the information content of these signals can impose high sampling requirements for digital detection techniques. Solvable chaotic oscillators have been proposed to address such issues due to their simple, matched filters, where hardware has been demonstrated with a bandwidth of 10-20 kHz.

Analytic solutions throughout a period doubling route to chaos.

We show examples of dynamical systems that can be solved analytically at any point along a period doubling route to chaos. Each system consists of a linear part oscillating about a set point and a nonlinear rule for regularly updating that set point. Previously it has been shown that such systems can be solved analytically even when the oscillations are chaotic.

A digital matched filter for reverse time chaos.

The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter.