When/where: Tues March 25, 2003, 4:15PM, Room 201 LOM

Speaker: Thao Nguyenn, City College of CUNY, School of Engineering

Title of talk: The tiling conjecture of feedback one-bit A/D converters

Abstract:

The current technology of analog-to-digital (A/D) conversion consists of highly oversampling a bandlimited input signal and converting it into a one-bit stream.

Using a feedback system empirically designed and optimized by engineers, the one-bit (or two-level) output is made so that its local time average approximately reconstructs the input amplitude value at every given instant. While this technique yields A/D converters of high performances in practice, there still exists little theory to predict these performances analytically. This is because the one-bit converter consists of a feedback system that includes a nonlinear operation, i.e., the one-bit quantization. This amounts to a dynamical system whose output is difficult to derive explicitly.

New theoretical results have been obtained as the state variables of the one-bit feedback system have been recently observed by Gunturk and Daubechies to remain in a "tile" set when the input is constant. This property has fundamental impacts as it enables the use of ergodic theory to perform error predictions. This talk will include two main aspects: - the origin of the tiling phenomenon, - the use of tiling for the mathematical prediction of the conversion error.