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Our research into the uses of chaotic systems in spread-spectrum communications has resulted in many significant and important advances, which have been documented in 39 published papers. These advances were made in categories critical to the successful future incorporation of chaos in communication systems such as: carrier design, cryptographic security, synchronization schemes, robustness analysis, channel capacity, commercial applications, and practical synchronization in real-world wireless environments. Both theoretical and practical aspects were considered, for example: An integrated circuit capable of producing chaotic and hyperchaotic signals was fabricated; An important theory of generalized synchronization between different chaotic systems was developed; a new, improved synchronization scheme called impulsive synchronization was invented, which has lead to the filing of a patent; and a method based on adaptive control theory was developed to efficiently cope with parameter drift in practical chaotic circuits and time-varying channel distortion.

The aim of this research project was to alleviate the tone problem in sigma delta modulators by exploiting chaos and unstable limit cycles. This was achieved by designing encoders with open loop poles outside the unit circle. A side effect of this approach is the possibility of the modulator becoming unstable, i.e., of the internal states becoming unbounded. An analysis of the stability characteristics and the tonal properties of the chaotic double loop sigma delta modulator was presented. Bounds on maximum internal states were determined. It was shown that the tone behavior of the double loop sigma delta modulator is improved when the poles are moved outside the unit circle; however, not all spectral peaks are removed. A mechanism for tone generation was identified and general spectral characteristics as a function of pole location were obtained. It was shown that there is a trade off between stability, tonal behavior and signal to noise ratio performance. Audio testing along with a series of simulations were also performed to compare the efficacy of pole placement with that of the more traditional tone removal technique of dithering. Based on the results, design guidelines were presented. In addition to the above results, a switched capacitor implementation of the double loop sigma delta modulator with open loop poles outside the unit circle was considered. Initial testing of the integrated circuit verified some of the theoretical results on the tonal behavior of the double loop sigma delta modulator.

The grant supported work in three dimensional image representation and reconstruction. Multilevel information is combined to enable effective representation of shading and occlusion. The modeling process fits in well with CCD camera array sensing, and multichannel sampling permits improved motion estimates between frames in a video sequence. The usual redundancy in 3-D scene representation can be shown to allow meaningful exploitation by encoding the redundant distance, depth and intensity parameters. Significant performance improvements were demonstrated over usual bilinear and cubic B-spline algorithms.

We have made impressive research progress on several related aspects of our research grant during the period; namely, (1) robustness of chaotic synchronization schemes, (2) efficiency of chaotic synchronization systems, (3) design of practical chaotic spread-spectrum communication systems, (4) channel capacity of chaotic spread-spectrum communication systems, and (5) potential commercial applications of chaotic spread spectrum communication systems.