2/27/03
MIT/HP Alliance Colloquium: "Curves
in Communications and Signal Processing"
Dr. Vinay Vaishampayan,
AT&T Shannon Labs, 34pm, 34101
Abstract:
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^{N1} 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.
