Stephen R. Addison

Characteristic functions in radar and sonar

We often encounter problems that involve either nonlinear or multi-dimensional combinations of random variables. One would like to be able to determine the probability density function of these combinations. The individual components that contribute to the combination are assumed known, but the combination is not known. Computations to determine this combined PDF axe tedious and difficult to accomplish in most cases. We propose a simpler means to bypass many of these difficulties. By using Fourier analysis and application of the definition of the Dirac delta function, the proper form the combined PDF is obtained with considerable simplification. The motivation for this is engineering applications that occur frequently in radar applications that involve combinations of probability density functions.

Chaos and Encryption: Problems and Potential

A brief introduction to the history of chaos and chaotic encryption is provided. Simple circuits that oscillate chaotically are reviewed. Methods of removing the masking produced by a single chaotic oscillator are reviewed. Methods that have been proposed to produce a secure encryption scheme using chaotic oscillators are described and evaluated. Based on the knowledge that only circuits with a single nonlinear element synchronize quickly enough to allow the encryption decryption of real-time communications, and that such schemes are inherently vulnerable to return map reconstruction, it appears that chaotic encryption will not be deployed in communications systems. However, systems with multiple nonlinearities continue to show some promise

Electrodynamic Focusing of Charged Aerosol Particles

An electrodynamic screen for focusing charged particles carried by an airflow stream has been constructed and tested. The screen has the shape of a cone frustum with half-angle of 8° and is 17 cm long. Entrance and exit diameters are 7.0 and 2.5 cm, respectively. Electrodes forming the screen are three 0.71-mm diameter stainless-steel wires configured as a triple-start helix with 2.0-mm pitch. A three-phase power supply drives each wire with a line-to-ground voltage of 2300 V at 350 Hz with a phase difference of 120° between adjacent wires. Test particles of 5.2-μm aerodynamic diameter with electric charge of 1850–6080 elementary units per particle in an aerosol having a mean flow velocity of 4.3×10−2 m/s parallel to the vertically oriented cone axis are confined and focused with essentially no particle loss. Minimum distance of approach of the test particles to the screen, as found from computer simulation of particle trajectories, solution of the particle equations of motion by linear approximation, and...

The Rayleigh problem is everywhere

In this work, we discuss a variety of problems that can be cast as specific instances of the superposition of random amplitudes times random phase functions, the Rayleigh problem. A wide number of problems that occur in sensor domain are equivalent to specific instances of this problem. Using characteristic functions, it is possible to determine how to mathematically characterize the probability density function or equivalently the characteristic function for the general Rayleigh problem.

Computing the characteristic function for sums of sinusoidal random variables

In this note we develop the methodology for computing the moments of the characteristic function for the superposition of sinusoidal transformed random variables. Thus we solve an important case of the Rayleigh problem, and point how to use this technique to completely solve it

Is extensivity a fundamental property of entropy

The role of linearity in the definition of entropy is examined. While discussions of entropy often treat extensivity as one of its fundamental properties, the extensivity of entropy is not axiomatic in thermodynamics. It is shown that systems in which entropy is an extensive quantity are systems in which a entropy obeys a generalized principle of linear superposition.

Symbolic Noise, Signal Processing, and Signal Enhancement by the Use of Chaos

In this paper, we discuss the symbolic and visual approach to combinations of noise plus noise. Just as in other application chaos is used to disguise noise, we suggest that their is a dual process where chaos may be used to amplify signals in noise. An example of this is presented and some of the implications are discussed

Chaotic encryption and decryption: involving undergraduates in authentic research

Research is becoming an integral part of the educational experiences of undergraduates. The University of Central Arkansas (UCA) has developed programs that provide authentic research experiences for undergraduate majors in its College of Natural Sciences in Mathematics. An investigation of chaotic encryption involves mentors from UCA and NSWCDD. Complex dynamical systems can be used to generate pseudorandom electronic signals. Such pseudorandom signals can be combined with communications signals to mask underlying signals. When broadcast, the resulting combination appears to be broadcast noise. In this project chaotic electric circuits are being used to mask information. Such circuits exhibit the property of chaotic synchronization. The synchronization is known to persist when communications signals are added to the chaotic signal produced by the source circuit. The students are investigating the stability of synchronization when different signal inputs are imposed on the circuits, and determining the conditions under which chaotic signals can be separated from underlying communication signals. Methods of determining which signals contain information are also being investigated.

Precision measurements of chaotic electric circuits

The construction and testing of a class of chaotic circuits corresponding to the differential equation xumldot = -Axuml - xdot + D(x) - alpha are described. In this equation D(x) represents the non-linear components that cause the circuit to oscillate chaotically. The suitability of circuits containing different non-linear elements as components in an analog encryption/decryption system is assessed

A methodology for characterizing phase noise in modulated radar waveforms: an alternative 'terrain' characterization method

The problem of modulated noise first arose in Lord Rayleighs investigations of acoustical backscatter off of rough sea surfaces. The same problem occurs in radar when the electromagnetic waveform takes an indirect return or transmit path to a scatterer (target) and then is received as a noise corrupted signal at the radar receiver. The effect is to produce modulated noise on the return signal. While most texts have a tendency to model the effect of noise as purely additive, it is more properly modeled as modulated noise. Recent work by the authors allow one to statistically characterize the effect of modulated noise on the received signal. This has some implications for phenomenology on being able to characterize radar backscatter from land, sea, weather as well as the implications for improved signal processing.