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MIT/HP Alliance Colloquium: "Curves in Communications and Signal Processing"
Dr. Vinay Vaishampayan, AT&T Shannon Labs, 3-4pm, 34-101

This talk is about bandwidth expansion maps, i.e., functions which map R to R^N, N>1. Such maps (curves) are studied in communication theory because they underlie nonlinear modulation systems such as frequency modulation. We address the following problem: on the sphere S^{N-1} in R^N, construct a curve of maximal length subject to a constraint on the minimum distance between its folds (which we define). A performance analysis is presented, optimal constructions are given and a decoding algorithm is developed. Interesting connections to shift dynamical systems, the cubic lattice (especially its projection into one lower dimension), and Nyquist rate A/D conversion are also highlighted. Finally, I will also review from the literature, some interesting applications of curves in statistics and signal processing.

Collaboration with: Sueli I. R. Costa and N. J. A. Sloane.

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