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. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

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. Here, an analog implementation of a four-state adaptive oscillator is presented for the first time as a field-programmable analog array (FPAA) circuit. The FPAA diagram is described, and the hardware performance is presented. This simple FPAA-based oscillator can be used as an analog frequency analyzer, as its frequency state will evolve to match the external forcing frequency. Notably, this is done without any analog-to-digital conversion or pre-processing, making it an ideal frequency analyzer for low-power and low-memory applications.

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. Notably, the adaptive oscillator learns parameters of external stimuli through its ability to completely synchronize without using any pre- or post-processing methods. Previously, Hopf oscillators have been built as two-state (a regular Hopf oscillator) and three-state (a Hopf oscillator with adaptive frequency) systems via VLSI and FPGA designs. Building on these important implementations, a continuous-time, analog circuit implementation of a Hopf oscillator with adaptive frequency and amplitude is achieved. The hardware measurements and SPICE simulation show good agreement. To demonstrate some of its functionality, the circuit's response to several complex waveforms, including the response of a square wave, a sawtooth wave, strain gauge data of an impact of a nonlinear beam, and audio data of a noisy microphone recording, are reported. By learning both the frequency and amplitude, this circuit could be used to enhance applications of AOs for robotic gait, clock oscillators, analog frequency analyzers, and energy harvesting.