Frank T. Werner

A Novel Third Order Analog Chaotic Oscillator

Chaotic oscillators, which are characterized by a spread spectrum response, have a wide range of possible applications including random number generation, communication systems, noise signal generation, and jamming. A novel chaotic oscillator design and implementation that reduces design complexity, component count, and size over a traditional approach is presented. The oscillator design approach can be divided into three primary subsystems. The first subsystem is called the stretching mechanism, which exhibits an exponential unstable sinusoidal response as a standalone system. This unstable subsystem is bounded by a feedback network. The feedback network consists of guard condition and a folding mechanism. The stretching mechanism will grow until a criterion for the guard condition is met which triggers when the folding mechanism should fold, or double. The motivation behind this design was inspired by the linear second-order set of differential equations with an exactly solvable solution. The electronic...

A 4 MHz Chaotic Oscillator Based on a Jerk System

Chaotic oscillators have a wide range of possible applications including random number generation (RNG), a stimulation source for characterization of MEMS devices, spread spectrum communications, and audio range and RF noise sources. Some distinct characteristics of chaotic systems include topological mixing, determinism, long-term aperiodic behavior, sensitivity to initial conditions, as well as a spread spectrum response. In particular, the aperiodic behavior and sensitivity to initial conditions make chaotic oscillators an ideal candidate for RNG. In practice, one of the more important aspects of a RNG is the speed at which data/bits can be generated. In electronics, as the frequency of operation increases, so do the design restrictions and challenges. In addition, many of these chaotic systems are based on nonlinearities or complex math functions that are difficult to implement in electronic circuitry. Through careful selection of the system’s structure, complex behavior can be achieved in electronic circuitry with minimized component count, footprint and power consumption. Additionally, this concept reduces the design complexity compared to traditional techniques, and the jerk chaos architecture can aid in increasing the fundamental frequency by minimizing feedback paths in the chaotic oscillator. Presented in this work is a printed circuit board electronic implementation of a 4 MHz chaotic jerk system that exhibits complex, rich dynamics using very simple electronic circuits.

A Matched Filter Developed for Chaotic Waveforms

A matched filter developed for use in chaos-based communications systems is presented. A matched filter is the optimum filter for maximizing the signal-to-noise ratio of a received signal in the presence of additive Gaussian white noise (AGWN). Chaos-based communications systems encode information into a chaotic waveform using arbitrary small perturbations to control the trajectory of the chaotic oscillator. Chaotic waveforms are deterministic, are sensitive to initial conditions, have aperiodic long-term behavior, have a spread frequency spectrum, and are theoretically immune to interference. There has been great interest in using chaotic waveforms in communication applications. One reason for this interest is that the spread spectrum of a chaotic waveform gives the appearance of noise when observed over a prolonged period of time. This masks the waveform from anyone without prior knowledge of its presence. Another reason is that to retrieve the information encoded in the chaotic waveform, complete knowl...